Final Project
Team13
2024-05-03
STAT515 Final Project
1.Introduction
Depression is one of the mental disorders affecting millions of people around the world. Public health needs to study and understand the causes of depression and its risk factors. Depression can have severe consequences on an individual’s life, and it will reduce life quality and increase the risk of suicide. Therefore, we have chosen to focus our efforts on investigating depression and the factors causing that. For this reason we decide to work on depression.
2.Background
As the prevalence of depression and anxiety disorders rises globally, we face increasing public health challenges. As shown in the figure, the prevalence of anxiety and depression varies significantly from country to country, suggesting the need to develop and implement effective treatment strategies tailored to each region. Global attention and treatment for depression and anxiety disorders is urgent, and we must take action to reduce the health burden of these disorders.
This visualization is an interactive map with the addition of the shiny feature, which means that we have taken into account the needs of some colorblind groups, and we can switch the background color at will so that different viewers can access the information in the graphic.
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## remotes::install_github('r-tmap/tmap')## tmap mode set to interactive viewingThis image is a world map showing the global prevalence of anxiety and depression. The different colors on the map represent the prevalence of anxiety and depression in different countries, ranging from 0% to 50%. For example, the dark red color represents a prevalence of 40% to 50%, while the light yellow color indicates a prevalence of 0% to 10%. As can be seen from the figure, anxiety and depression are unevenly distributed globally, with some countries having significantly higher prevalence rates than others.
3.Depression Dataset
3.1.1 Introduction of Dataset
3.1.2 structure of dataset
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## layout3.2 Explore the data
3.2.1 Box plot and Bar plot.
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3.2.2 HeatMap
This heat map shows the correlations between variables, where shades of color indicate differences in the strength of the correlation. Many of the darker colored grids in the heat map indicate weaker correlations between these variables. For this reason we determined the direction of our research
1. low correlation between some of the data features: this affects the predictive performance of the linear model and given the presence of some categorical variables we will use logistic regression models and decision tree models.
2. category imbalance: there are particularly few non-depression categories in this dataset, which makes it difficult for the model to learn valid patterns from the data, and therefore the correlation matrix may show weak correlations (we demonstrate this later in the model, indicates a high rate of false positives.). In this case, the use of techniques such as SMOTE may help to enhance the performance of the model by balancing the categories to allow the model to better learn a small number of classes.
3. the need for data preprocessing: there are no NULL values in this dataset, but a large number of 0 values appear. For this we need a study to explore the meaning of 0 values and process them .
4. Data preprocessing
4.1 PCA
4.1.1 PCA application
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 2.5159 1.76735 1.62361 1.56583 1.39430 1.34675 1.22116
## Proportion of Variance 0.1862 0.09187 0.07753 0.07211 0.05718 0.05335 0.04386
## Cumulative Proportion 0.1862 0.27804 0.35557 0.42769 0.48487 0.53821 0.58207
## PC8 PC9 PC10 PC11 PC12 PC13 PC14
## Standard deviation 1.13455 1.06340 1.03218 1.02295 0.95435 0.94237 0.92951
## Proportion of Variance 0.03786 0.03326 0.03133 0.03078 0.02679 0.02612 0.02541
## Cumulative Proportion 0.61993 0.65319 0.68452 0.71530 0.74209 0.76821 0.79362
## PC15 PC16 PC17 PC18 PC19 PC20 PC21
## Standard deviation 0.90396 0.8882 0.81877 0.80343 0.78846 0.75410 0.74131
## Proportion of Variance 0.02403 0.0232 0.01972 0.01899 0.01828 0.01673 0.01616
## Cumulative Proportion 0.81765 0.8409 0.86057 0.87956 0.89784 0.91457 0.93073
## PC22 PC23 PC24 PC25 PC26 PC27 PC28
## Standard deviation 0.68170 0.64688 0.60510 0.54098 0.48887 0.45130 0.42257
## Proportion of Variance 0.01367 0.01231 0.01077 0.00861 0.00703 0.00599 0.00525
## Cumulative Proportion 0.94440 0.95671 0.96748 0.97608 0.98311 0.98910 0.99436
## PC29 PC30 PC31 PC32 PC33 PC34
## Standard deviation 0.35686 0.22364 0.10839 0.05292 0.001526 2.008e-08
## Proportion of Variance 0.00375 0.00147 0.00035 0.00008 0.000000 0.000e+00
## Cumulative Proportion 0.99810 0.99957 0.99992 1.00000 1.000000 1.000e+00## [1] 0.1861730 0.2780412 0.3555743 0.4276868 0.4848652 0.5382108 0.5820708
## [8] 0.6199299 0.6531895 0.6845244 0.7153017 0.7420895 0.7682092 0.7936207
## [15] 0.8176543 0.8408564 0.8605737 0.8795590 0.8978435 0.9145692 0.9307322
## [22] 0.9444003 0.9567076 0.9674765 0.9760841 0.9831133 0.9891037 0.9943555
## [29] 0.9981010 0.9995720 0.9999176 0.9999999 1.0000000 1.0000000## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 418 92
## 1 5 1
##
## Accuracy : 0.812
## 95% CI : (0.7756, 0.8448)
## No Information Rate : 0.8198
## P-Value [Acc > NIR] : 0.7
##
## Kappa : -0.0017
##
## Mcnemar's Test P-Value : <2e-16
##
## Sensitivity : 0.98818
## Specificity : 0.01075
## Pos Pred Value : 0.81961
## Neg Pred Value : 0.16667
## Prevalence : 0.81977
## Detection Rate : 0.81008
## Detection Prevalence : 0.98837
## Balanced Accuracy : 0.49947
##
## 'Positive' Class : 0
## 4.1.2 PCA result analysis
1. Explanatory power of PCA: From the result given by the principal component analysis, the proportion of cumulative variance explained by the first 15 principal components is about 97.36%. This means that most of the information is contained by these 15 components, which, theoretically, is a better data downscaling.
2. model performance (using the properties of PCA):
Confusion matrix: the results show that the model predicted almost all the test samples to be in the negative category (non-depressed) and only one sample was predicted to be in the positive category (depressed), but this prediction was wrong. In fact, there should be 38 positive samples.
Accuracy and sensitivity: the overall accuracy of the model was 82.89%, but the specificity of the model was 0, indicating that it failed to correctly identify any truly depressed samples. This indicates a high rate of false positives.
3. problem analysis:
Data imbalance: the proportion of depressed and non-depressed samples in the dataset is severely imbalanced, and the model will be biased towards the majority class, resulting in high precision but low recall.
Influence of data: although PCA can reduce the dimensionality of the data, the correlation between the original variables is not high enough for PCA to effectively capture information useful for prediction. In addition, the inclusion of a large number of zero values in many variables may affect the effectiveness of PCA because these zeros may represent different meanings (e.g., not recorded or actual value of zero), thus distorting the intrinsic distribution of the data.PCA tends to emphasize variables with large variance. There are some variables in this dataset that have very high variance (e.g., agricultural income) and others that have relatively low variance, then in PCA the There are some variables in this dataset that have very high variance (e.g., agricultural income) and others that have relatively low variance, then in PCA the variables with large variance will have a large impact on the calculation of the principal components, resulting in these principal components reflecting mainly information from the variables with large variance and ignoring other variables that may be just as important, but with low variance.
4. Improve the methodology:
Dealing with the imbanlanced data: As we can see, the visualizations show us the dataset is imbalanced. We are considering use SMOTE or sampling techniques to balance the categories in this dataset, especially our target variable: depression status is highly imbalanced in categories.
Feature engineering: further analyze the variables, especially those containing a large number of 0 values, to understand the specific meaning of these 0 values and consider whether these variables need special treatment, such as variable transformation, filling in missing values, etc.
4.2 Remove the outliers
In the preprocessing stage, removing outliers is of significant importance. Numerous techniques are available for this purpose, and in our project, we opted for the Z-score method. By leveraging the mean and standard deviation of the dataset, this method ensures a confidence level equivalent to 99.7%.
4.2.1 cleaned_dataset
## 'data.frame': 1147 obs. of 35 variables:
## $ sex : int 1 1 1 1 1 1 1 1 0 1 ...
## $ age : num 21 44 23 67 28 23 22 27 59 35 ...
## $ marital_status : int 0 1 1 0 1 1 1 1 0 1 ...
## $ children : int 3 6 1 0 4 3 3 2 4 6 ...
## $ household_size : int 4 8 3 1 6 5 5 4 6 8 ...
## $ years_of_edu : int 10 6 7 1 10 8 9 10 10 10 ...
## $ hh_children : int 3 6 1 0 0 0 0 2 4 6 ...
## $ cons_nondurable : num 358 233 172 37 0 ...
## $ asset_durable : num 208.2 11.7 120.9 32.8 0 ...
## $ asset_phone : num 40 0 56.1 0 0 ...
## $ asset_savings : num 0 12.8 0 0 0 ...
## $ asset_land_owned_total: num 2 3 0 1.75 0 0 0 0 0.5 1.7 ...
## $ cons_allfood : num 231 211.9 81.6 25.7 0 ...
## $ cons_alcohol : num 0 1.17 0 0 0 ...
## $ cons_tobacco : num 0 0 0 0 0 ...
## $ cons_med_total : num 0 0 0 0 0 ...
## $ cons_med_children : num 0 0 0 0 1.22 ...
## $ cons_ed : num 0 1.521 0.721 0 0 ...
## $ cons_social : num 4 0 13.45 2.54 0 ...
## $ cons_other : num 122.84 19.97 76.15 8.73 0 ...
## $ ent_nonag_revenue : num 72.1 0 0 0 0 ...
## $ ent_nonag_flowcost : num 24 0 0 0 0 ...
## $ ent_total_cost : num 48.166 0.378 0 4.805 0 ...
## $ fs_adwholed_often : num 0 0 0 3 0 0 0 0 0 3 ...
## $ fs_chwholed_often : num 0 0 0 0 0.504 ...
## $ fs_meat : num 3 5 2 1 3.07 ...
## $ fs_enoughtom : num 0 0 0 0 0 0 0 1 0 1 ...
## $ fs_sleephun : num 1 0 1 1 0 0 0 1 0 1 ...
## $ med_sickdays_hhave : num 1 2.75 2.67 3 1.44 ...
## $ med_u5_deaths : num 0 0 0 0 0 0 0 0 0 0 ...
## $ ed_expenses : num 0 18.26 8.65 0 0 ...
## $ ed_schoolattend : num 0 0.8 1 0 0 ...
## $ durable_investment : num 569.9 252.7 141.7 58.3 0 ...
## $ nondurable_investment : num 48.166 14.712 0.721 4.805 0 ...
## $ depression : num 0 0 0 1 0 1 0 0 0 0 ...## sex age marital_status
## TRUE TRUE TRUE
## children household_size years_of_edu
## TRUE TRUE TRUE
## hh_children cons_nondurable asset_durable
## TRUE TRUE TRUE
## asset_phone asset_savings asset_land_owned_total
## TRUE TRUE TRUE
## cons_allfood cons_alcohol cons_tobacco
## TRUE TRUE TRUE
## cons_med_total cons_med_children cons_ed
## TRUE TRUE TRUE
## cons_social cons_other ent_nonag_revenue
## TRUE TRUE TRUE
## ent_nonag_flowcost ent_total_cost fs_adwholed_often
## TRUE TRUE TRUE
## fs_chwholed_often fs_meat fs_enoughtom
## TRUE TRUE TRUE
## fs_sleephun med_sickdays_hhave med_u5_deaths
## TRUE TRUE TRUE
## ed_expenses ed_schoolattend durable_investment
## TRUE TRUE TRUE
## nondurable_investment depression
## TRUE TRUE## sex age marital_status children
## sex 1.000000000 -0.136329281 0.27351242 0.2235183786
## age -0.136329281 1.000000000 -0.40009835 -0.1122369397
## marital_status 0.273512416 -0.400098351 1.00000000 0.2213770708
## children 0.223518379 -0.112236940 0.22137707 1.0000000000
## household_size 0.255252384 -0.069977261 0.32478405 0.9348874419
## years_of_edu -0.076007865 -0.396506438 0.19905840 0.1635600948
## hh_children 0.197450150 -0.071031539 0.15366930 0.6369515831
## cons_nondurable 0.075544133 -0.030918410 0.15027328 0.0885514198
## asset_durable 0.079719412 -0.090569900 0.12976656 0.0532511254
## asset_phone 0.146373413 -0.185179059 0.18265302 0.0818207541
## asset_savings 0.004742042 -0.013258537 0.03104469 -0.0046487712
## asset_land_owned_total -0.010935527 0.256278615 -0.06060419 -0.0486652177
## cons_allfood 0.077389856 -0.026222298 0.13473087 0.0693714365
## cons_alcohol -0.036498211 0.016826151 0.06514488 -0.0033885692
## cons_tobacco -0.017540174 0.062568688 0.05734993 0.0209312796
## cons_med_total -0.104872487 0.016557203 0.08105429 0.0006077517
## cons_med_children -0.125741746 0.024128426 0.05199862 0.0282779995
## cons_ed 0.045205835 0.136085173 0.03259242 0.1394922162
## cons_social 0.068544257 -0.034876686 0.06504699 0.0420738659
## cons_other 0.084473371 -0.094560519 0.11707611 0.1037599523
## ent_nonag_revenue 0.037908468 -0.019200138 -0.05142287 0.0426702715
## ent_nonag_flowcost 0.046117780 -0.022769838 -0.05182265 0.0389417970
## ent_total_cost 0.051106928 -0.021587201 -0.04375056 0.0432178223
## fs_adwholed_often -0.025735795 0.177070258 -0.11757884 -0.0158685586
## fs_chwholed_often 0.032672346 0.082337308 -0.01532264 0.0944021589
## fs_meat -0.019492346 -0.048549047 0.05497803 0.0001027198
## fs_enoughtom 0.067151860 -0.059864081 0.06155151 -0.0162940716
## fs_sleephun 0.006099500 0.124709659 -0.08256889 -0.0049687286
## med_sickdays_hhave -0.092736460 0.204572737 -0.16532619 -0.2298859774
## med_u5_deaths 0.042598585 -0.097040359 0.08495699 -0.0639881754
## ed_expenses 0.048682509 0.107937400 0.03391059 0.1693412422
## ed_schoolattend 0.158867156 0.010671546 0.04596508 0.2560814444
## durable_investment 0.109633619 -0.009946984 0.13200595 0.0725051879
## nondurable_investment 0.044284961 -0.015760895 -0.01258186 0.0385884155
## depression -0.007864312 0.104586878 -0.08135822 0.0093130715
## household_size years_of_edu hh_children
## sex 0.2552523839 -0.076007865 1.974502e-01
## age -0.0699772611 -0.396506438 -7.103154e-02
## marital_status 0.3247840526 0.199058397 1.536693e-01
## children 0.9348874419 0.163560095 6.369516e-01
## household_size 1.0000000000 0.133991220 6.180790e-01
## years_of_edu 0.1339912201 1.000000000 8.929514e-02
## hh_children 0.6180789557 0.089295136 1.000000e+00
## cons_nondurable 0.1437222124 0.069834490 4.630234e-01
## asset_durable 0.0935210875 0.162811265 3.602833e-01
## asset_phone 0.1170388024 0.165127878 3.667773e-01
## asset_savings 0.0043669668 0.073918494 4.915296e-02
## asset_land_owned_total 0.0053866003 -0.111563942 1.879720e-01
## cons_allfood 0.1203352412 0.039645363 4.123813e-01
## cons_alcohol 0.0122955425 -0.010042348 7.091114e-02
## cons_tobacco 0.0400518195 -0.034187781 1.160074e-01
## cons_med_total 0.0252185584 0.099440142 9.257147e-02
## cons_med_children 0.0520810853 0.097327839 2.017262e-02
## cons_ed 0.1893597383 -0.004611074 2.671770e-01
## cons_social 0.0658872107 0.077059530 2.393156e-01
## cons_other 0.1337700099 0.128357993 4.131048e-01
## ent_nonag_revenue 0.0239992231 0.037650959 9.529252e-02
## ent_nonag_flowcost 0.0293371793 0.065584958 1.073105e-01
## ent_total_cost 0.0360217142 0.068727241 1.274923e-01
## fs_adwholed_often -0.0292993730 -0.074643503 1.315172e-01
## fs_chwholed_often 0.0803987262 -0.021563508 6.247656e-02
## fs_meat 0.0056533046 0.005143384 9.411094e-05
## fs_enoughtom 0.0006370245 0.047467346 1.887765e-01
## fs_sleephun -0.0037211053 -0.098001282 2.429133e-01
## med_sickdays_hhave -0.2533737057 -0.128186650 -1.498050e-01
## med_u5_deaths -0.0412230032 -0.012647319 2.988938e-02
## ed_expenses 0.2063735270 0.016080849 3.005115e-01
## ed_schoolattend 0.2794054024 0.041076636 6.675593e-01
## durable_investment 0.1199287201 0.093549064 3.781532e-01
## nondurable_investment 0.0416125923 0.095695750 1.422898e-01
## depression 0.0020570582 -0.126243493 4.738743e-03
## cons_nondurable asset_durable asset_phone asset_savings
## sex 0.075544133 0.07971941 0.14637341 0.004742042
## age -0.030918410 -0.09056990 -0.18517906 -0.013258537
## marital_status 0.150273280 0.12976656 0.18265302 0.031044685
## children 0.088551420 0.05325113 0.08182075 -0.004648771
## household_size 0.143722212 0.09352109 0.11703880 0.004366967
## years_of_edu 0.069834490 0.16281127 0.16512788 0.073918494
## hh_children 0.463023399 0.36028329 0.36677729 0.049152959
## cons_nondurable 1.000000000 0.44260580 0.39682862 0.117579359
## asset_durable 0.442605797 1.00000000 0.49932481 0.268743316
## asset_phone 0.396828619 0.49932481 1.00000000 0.124437451
## asset_savings 0.117579359 0.26874332 0.12443745 1.000000000
## asset_land_owned_total 0.247368822 0.16229855 0.06397891 0.016327399
## cons_allfood 0.966451134 0.38704219 0.33332285 0.087968572
## cons_alcohol 0.244126180 0.03295366 -0.02207446 -0.005041868
## cons_tobacco 0.226869151 0.03559299 -0.01579521 0.010629950
## cons_med_total 0.314684586 0.11938720 0.07360623 0.003439300
## cons_med_children 0.191441649 0.04138057 0.02349999 0.001116218
## cons_ed 0.275967835 0.15840657 0.27211681 0.155487327
## cons_social 0.367013887 0.30281759 0.23643087 0.115968420
## cons_other 0.646331813 0.43325129 0.44569583 0.147054846
## ent_nonag_revenue 0.095780463 0.09550633 0.08172755 0.016340257
## ent_nonag_flowcost 0.103552316 0.13975557 0.18084418 0.046014193
## ent_total_cost 0.140754042 0.16546590 0.20188891 0.057165530
## fs_adwholed_often 0.046922114 -0.01941714 -0.03984742 -0.015823192
## fs_chwholed_often -0.030576510 -0.07280189 -0.07976236 -0.019647063
## fs_meat 0.112228106 0.06448843 -0.03484732 -0.018140530
## fs_enoughtom 0.255075344 0.23659578 0.24016406 0.041759047
## fs_sleephun 0.162589103 0.02511811 0.04113945 -0.010747829
## med_sickdays_hhave -0.008993309 -0.07843424 -0.04943072 -0.033227273
## med_u5_deaths 0.101577790 0.05067042 0.05474938 -0.010191622
## ed_expenses 0.291615160 0.15905972 0.29116466 0.167918539
## ed_schoolattend 0.465165658 0.37999575 0.34876475 0.036464076
## durable_investment 0.492244105 0.77609034 0.40644038 0.257011353
## nondurable_investment 0.193600512 0.29497134 0.24368018 0.648200858
## depression -0.023045708 -0.04797939 -0.03893431 -0.011961091
## asset_land_owned_total cons_allfood cons_alcohol
## sex -0.01093553 0.07738986 -0.036498211
## age 0.25627861 -0.02622230 0.016826151
## marital_status -0.06060419 0.13473087 0.065144877
## children -0.04866522 0.06937144 -0.003388569
## household_size 0.00538660 0.12033524 0.012295542
## years_of_edu -0.11156394 0.03964536 -0.010042348
## hh_children 0.18797196 0.41238130 0.070911138
## cons_nondurable 0.24736882 0.96645113 0.244126180
## asset_durable 0.16229855 0.38704219 0.032953660
## asset_phone 0.06397891 0.33332285 -0.022074460
## asset_savings 0.01632740 0.08796857 -0.005041868
## asset_land_owned_total 1.00000000 0.23271245 0.063913919
## cons_allfood 0.23271245 1.00000000 0.185506672
## cons_alcohol 0.06391392 0.18550667 1.000000000
## cons_tobacco 0.09402880 0.18295743 0.502605353
## cons_med_total 0.06147515 0.18584180 0.134946387
## cons_med_children 0.02732393 0.07926619 0.068029884
## cons_ed 0.12545505 0.20054551 0.024306976
## cons_social 0.10834378 0.26641775 0.036464179
## cons_other 0.16725163 0.46836751 0.101625499
## ent_nonag_revenue 0.01324190 0.05225984 -0.012543798
## ent_nonag_flowcost 0.01585542 0.07865089 -0.017115253
## ent_total_cost 0.03064688 0.11290094 -0.012449977
## fs_adwholed_often 0.14552518 0.03672290 0.013146876
## fs_chwholed_often 0.01582205 -0.03405814 -0.021196950
## fs_meat 0.03132778 0.09854554 0.126341951
## fs_enoughtom 0.13028491 0.22580756 0.034942482
## fs_sleephun 0.18034645 0.15122503 0.037142748
## med_sickdays_hhave 0.04628771 -0.01849022 0.028068731
## med_u5_deaths 0.01897216 0.06631980 0.198556064
## ed_expenses 0.10082290 0.21840627 0.023067379
## ed_schoolattend 0.20008855 0.42632177 0.052493236
## durable_investment 0.25576878 0.45779919 0.039463321
## nondurable_investment 0.04069567 0.15021993 -0.010906572
## depression 0.01096124 -0.02350565 0.042121172
## cons_tobacco cons_med_total cons_med_children
## sex -0.0175401741 -0.1048724867 -0.1257417460
## age 0.0625686885 0.0165572033 0.0241284261
## marital_status 0.0573499291 0.0810542890 0.0519986162
## children 0.0209312796 0.0006077517 0.0282779995
## household_size 0.0400518195 0.0252185584 0.0520810853
## years_of_edu -0.0341877809 0.0994401422 0.0973278393
## hh_children 0.1160073818 0.0925714682 0.0201726238
## cons_nondurable 0.2268691507 0.3146845860 0.1914416493
## asset_durable 0.0355929853 0.1193871972 0.0413805697
## asset_phone -0.0157952145 0.0736062280 0.0234999920
## asset_savings 0.0106299497 0.0034392999 0.0011162182
## asset_land_owned_total 0.0940288005 0.0614751461 0.0273239283
## cons_allfood 0.1829574311 0.1858418009 0.0792661942
## cons_alcohol 0.5026053525 0.1349463873 0.0680298840
## cons_tobacco 1.0000000000 0.0719252442 0.0126404776
## cons_med_total 0.0719252442 1.0000000000 0.7792911115
## cons_med_children 0.0126404776 0.7792911115 1.0000000000
## cons_ed 0.0941021639 0.0569848480 0.0584086055
## cons_social 0.0309225723 0.1307350466 0.0667593708
## cons_other 0.1034908050 0.2855831866 0.2391992748
## ent_nonag_revenue -0.0066277729 0.0038541657 -0.0012223591
## ent_nonag_flowcost -0.0054646436 0.0252404456 0.0029284686
## ent_total_cost -0.0007553423 0.0349950410 0.0080527164
## fs_adwholed_often 0.0524480332 -0.0006815192 -0.0309301807
## fs_chwholed_often 0.0200372006 -0.0255437548 -0.0251468664
## fs_meat 0.1005412728 0.1093533902 0.0498740301
## fs_enoughtom 0.0464868087 0.0257174322 0.0143536900
## fs_sleephun 0.1123748169 0.0510615575 -0.0113235128
## med_sickdays_hhave 0.0279649144 0.1386186377 0.0434055344
## med_u5_deaths 0.1177856759 0.0571678294 0.0002486552
## ed_expenses 0.0913978574 0.0637326255 0.0660529705
## ed_schoolattend 0.0882712527 0.1154333560 0.0603528471
## durable_investment 0.0423857944 0.0808779207 0.0203987673
## nondurable_investment 0.0116056837 0.0320561146 0.0103851547
## depression 0.0075174326 0.0221150547 0.0127304276
## cons_ed cons_social cons_other ent_nonag_revenue
## sex 0.045205835 0.06854426 0.08447337 0.037908468
## age 0.136085173 -0.03487669 -0.09456052 -0.019200138
## marital_status 0.032592424 0.06504699 0.11707611 -0.051422866
## children 0.139492216 0.04207387 0.10375995 0.042670272
## household_size 0.189359738 0.06588721 0.13377001 0.023999223
## years_of_edu -0.004611074 0.07705953 0.12835799 0.037650959
## hh_children 0.267177027 0.23931561 0.41310477 0.095292518
## cons_nondurable 0.275967835 0.36701389 0.64633181 0.095780463
## asset_durable 0.158406566 0.30281759 0.43325129 0.095506333
## asset_phone 0.272116811 0.23643087 0.44569583 0.081727551
## asset_savings 0.155487327 0.11596842 0.14705485 0.016340257
## asset_land_owned_total 0.125455052 0.10834378 0.16725163 0.013241904
## cons_allfood 0.200545514 0.26641775 0.46836751 0.052259845
## cons_alcohol 0.024306976 0.03646418 0.10162550 -0.012543798
## cons_tobacco 0.094102164 0.03092257 0.10349081 -0.006627773
## cons_med_total 0.056984848 0.13073505 0.28558319 0.003854166
## cons_med_children 0.058408605 0.06675937 0.23919927 -0.001222359
## cons_ed 1.000000000 0.19281115 0.16976686 0.026746125
## cons_social 0.192811146 1.00000000 0.34558889 0.100996801
## cons_other 0.169766865 0.34558889 1.00000000 0.228142993
## ent_nonag_revenue 0.026746125 0.10099680 0.22814299 1.000000000
## ent_nonag_flowcost 0.057504433 0.12752960 0.13639899 0.564953185
## ent_total_cost 0.072102693 0.15161507 0.16542771 0.565750337
## fs_adwholed_often 0.082810120 0.01929808 0.04653217 0.170287252
## fs_chwholed_often 0.048097379 0.01403319 -0.01714582 -0.030269601
## fs_meat -0.041333167 0.02076895 0.07691808 0.028099526
## fs_enoughtom 0.037661735 0.16629961 0.26905531 0.064079249
## fs_sleephun 0.096060425 0.08164118 0.10218572 -0.021059473
## med_sickdays_hhave -0.031241762 -0.02306961 -0.02347482 -0.039512111
## med_u5_deaths -0.011135655 0.17452733 0.10810966 0.003023409
## ed_expenses 0.932086917 0.20766443 0.18847510 0.030952045
## ed_schoolattend 0.261744320 0.23473849 0.36779176 0.084188394
## durable_investment 0.211327294 0.34838415 0.38004750 0.094004667
## nondurable_investment 0.209248308 0.19568712 0.22320715 0.439267596
## depression 0.005230865 -0.01787429 -0.03537107 -0.013235113
## ent_nonag_flowcost ent_total_cost fs_adwholed_often
## sex 0.046117780 0.0511069280 -0.0257357950
## age -0.022769838 -0.0215872006 0.1770702578
## marital_status -0.051822652 -0.0437505578 -0.1175788363
## children 0.038941797 0.0432178223 -0.0158685586
## household_size 0.029337179 0.0360217142 -0.0292993730
## years_of_edu 0.065584958 0.0687272406 -0.0746435034
## hh_children 0.107310547 0.1274922800 0.1315172316
## cons_nondurable 0.103552316 0.1407540419 0.0469221139
## asset_durable 0.139755572 0.1654659009 -0.0194171359
## asset_phone 0.180844181 0.2018889144 -0.0398474210
## asset_savings 0.046014193 0.0571655304 -0.0158231919
## asset_land_owned_total 0.015855423 0.0306468790 0.1455251756
## cons_allfood 0.078650890 0.1129009371 0.0367229003
## cons_alcohol -0.017115253 -0.0124499772 0.0131468760
## cons_tobacco -0.005464644 -0.0007553423 0.0524480332
## cons_med_total 0.025240446 0.0349950410 -0.0006815192
## cons_med_children 0.002928469 0.0080527164 -0.0309301807
## cons_ed 0.057504433 0.0721026929 0.0828101197
## cons_social 0.127529600 0.1516150670 0.0192980819
## cons_other 0.136398994 0.1654277127 0.0465321700
## ent_nonag_revenue 0.564953185 0.5657503370 0.1702872519
## ent_nonag_flowcost 1.000000000 0.9969816926 0.0097189489
## ent_total_cost 0.996981693 1.0000000000 0.0105675360
## fs_adwholed_often 0.009718949 0.0105675360 1.0000000000
## fs_chwholed_often -0.037625415 -0.0382841831 0.5425710592
## fs_meat 0.079025266 0.0806493905 -0.1340449846
## fs_enoughtom 0.074181063 0.0869145220 -0.0506673422
## fs_sleephun -0.012308726 -0.0049587045 0.3822554618
## med_sickdays_hhave -0.017630569 -0.0153623822 0.1360304798
## med_u5_deaths 0.004037221 0.0059919905 0.0091447394
## ed_expenses 0.061693592 0.0763514717 0.0906725199
## ed_schoolattend 0.120118431 0.1403973120 0.1428906028
## durable_investment 0.135622413 0.1746417045 -0.0140809629
## nondurable_investment 0.784985236 0.7948137557 0.0037197249
## depression -0.035796973 -0.0378227725 0.1450221967
## fs_chwholed_often fs_meat fs_enoughtom
## sex 0.032672346 -1.949235e-02 0.0671518599
## age 0.082337308 -4.854905e-02 -0.0598640806
## marital_status -0.015322635 5.497803e-02 0.0615515104
## children 0.094402159 1.027198e-04 -0.0162940716
## household_size 0.080398726 5.653305e-03 0.0006370245
## years_of_edu -0.021563508 5.143384e-03 0.0474673461
## hh_children 0.062476564 9.411094e-05 0.1887764518
## cons_nondurable -0.030576510 1.122281e-01 0.2550753442
## asset_durable -0.072801888 6.448843e-02 0.2365957828
## asset_phone -0.079762362 -3.484732e-02 0.2401640635
## asset_savings -0.019647063 -1.814053e-02 0.0417590469
## asset_land_owned_total 0.015822048 3.132778e-02 0.1302849086
## cons_allfood -0.034058140 9.854554e-02 0.2258075564
## cons_alcohol -0.021196950 1.263420e-01 0.0349424823
## cons_tobacco 0.020037201 1.005413e-01 0.0464868087
## cons_med_total -0.025543755 1.093534e-01 0.0257174322
## cons_med_children -0.025146866 4.987403e-02 0.0143536900
## cons_ed 0.048097379 -4.133317e-02 0.0376617349
## cons_social 0.014033191 2.076895e-02 0.1662996123
## cons_other -0.017145817 7.691808e-02 0.2690553137
## ent_nonag_revenue -0.030269601 2.809953e-02 0.0640792492
## ent_nonag_flowcost -0.037625415 7.902527e-02 0.0741810632
## ent_total_cost -0.038284183 8.064939e-02 0.0869145220
## fs_adwholed_often 0.542571059 -1.340450e-01 -0.0506673422
## fs_chwholed_often 1.000000000 -7.399030e-02 -0.0831790470
## fs_meat -0.073990305 1.000000e+00 0.0794455769
## fs_enoughtom -0.083179047 7.944558e-02 1.0000000000
## fs_sleephun 0.184778164 -1.216907e-01 -0.1208344766
## med_sickdays_hhave -0.004417657 3.212457e-03 -0.0755126046
## med_u5_deaths 0.006057373 4.229920e-03 0.0164768184
## ed_expenses 0.053368945 -4.436123e-02 0.0143314940
## ed_schoolattend 0.102065060 -6.065066e-03 0.1622906795
## durable_investment -0.064374306 4.887798e-02 0.2552065531
## nondurable_investment -0.037660830 4.762709e-02 0.0929336964
## depression 0.066157458 1.771539e-02 -0.0208881386
## fs_sleephun med_sickdays_hhave med_u5_deaths
## sex 0.006099500 -0.0927364596 0.0425985853
## age 0.124709659 0.2045727368 -0.0970403586
## marital_status -0.082568890 -0.1653261926 0.0849569889
## children -0.004968729 -0.2298859774 -0.0639881754
## household_size -0.003721105 -0.2533737057 -0.0412230032
## years_of_edu -0.098001282 -0.1281866501 -0.0126473194
## hh_children 0.242913301 -0.1498050212 0.0298893786
## cons_nondurable 0.162589103 -0.0089933088 0.1015777896
## asset_durable 0.025118106 -0.0784342418 0.0506704246
## asset_phone 0.041139450 -0.0494307200 0.0547493819
## asset_savings -0.010747829 -0.0332272730 -0.0101916217
## asset_land_owned_total 0.180346449 0.0462877072 0.0189721645
## cons_allfood 0.151225034 -0.0184902188 0.0663198015
## cons_alcohol 0.037142748 0.0280687310 0.1985560641
## cons_tobacco 0.112374817 0.0279649144 0.1177856759
## cons_med_total 0.051061557 0.1386186377 0.0571678294
## cons_med_children -0.011323513 0.0434055344 0.0002486552
## cons_ed 0.096060425 -0.0312417616 -0.0111356555
## cons_social 0.081641183 -0.0230696113 0.1745273254
## cons_other 0.102185717 -0.0234748189 0.1081096648
## ent_nonag_revenue -0.021059473 -0.0395121110 0.0030234086
## ent_nonag_flowcost -0.012308726 -0.0176305685 0.0040372210
## ent_total_cost -0.004958705 -0.0153623822 0.0059919905
## fs_adwholed_often 0.382255462 0.1360304798 0.0091447394
## fs_chwholed_often 0.184778164 -0.0044176570 0.0060573727
## fs_meat -0.121690697 0.0032124566 0.0042299197
## fs_enoughtom -0.120834477 -0.0755126046 0.0164768184
## fs_sleephun 1.000000000 0.1109367855 0.0569282281
## med_sickdays_hhave 0.110936786 1.0000000000 -0.0005615704
## med_u5_deaths 0.056928228 -0.0005615704 1.0000000000
## ed_expenses 0.109207431 -0.0394202498 -0.0032002959
## ed_schoolattend 0.267136054 -0.1183477689 0.0799009697
## durable_investment 0.031104957 -0.0800212211 0.0268125273
## nondurable_investment -0.004177845 -0.0333406914 -0.0022274803
## depression 0.017246050 0.0604360210 -0.0143394154
## ed_expenses ed_schoolattend durable_investment
## sex 0.048682509 0.158867156 0.109633619
## age 0.107937400 0.010671546 -0.009946984
## marital_status 0.033910593 0.045965077 0.132005951
## children 0.169341242 0.256081444 0.072505188
## household_size 0.206373527 0.279405402 0.119928720
## years_of_edu 0.016080849 0.041076636 0.093549064
## hh_children 0.300511514 0.667559294 0.378153225
## cons_nondurable 0.291615160 0.465165658 0.492244105
## asset_durable 0.159059724 0.379995753 0.776090343
## asset_phone 0.291164663 0.348764754 0.406440378
## asset_savings 0.167918539 0.036464076 0.257011353
## asset_land_owned_total 0.100822898 0.200088550 0.255768780
## cons_allfood 0.218406274 0.426321774 0.457799192
## cons_alcohol 0.023067379 0.052493236 0.039463321
## cons_tobacco 0.091397857 0.088271253 0.042385794
## cons_med_total 0.063732626 0.115433356 0.080877921
## cons_med_children 0.066052971 0.060352847 0.020398767
## cons_ed 0.932086917 0.261744320 0.211327294
## cons_social 0.207664428 0.234738494 0.348384149
## cons_other 0.188475100 0.367791765 0.380047503
## ent_nonag_revenue 0.030952045 0.084188394 0.094004667
## ent_nonag_flowcost 0.061693592 0.120118431 0.135622413
## ent_total_cost 0.076351472 0.140397312 0.174641704
## fs_adwholed_often 0.090672520 0.142890603 -0.014080963
## fs_chwholed_often 0.053368945 0.102065060 -0.064374306
## fs_meat -0.044361226 -0.006065066 0.048877976
## fs_enoughtom 0.014331494 0.162290679 0.255206553
## fs_sleephun 0.109207431 0.267136054 0.031104957
## med_sickdays_hhave -0.039420250 -0.118347769 -0.080021221
## med_u5_deaths -0.003200296 0.079900970 0.026812527
## ed_expenses 1.000000000 0.305664668 0.206323141
## ed_schoolattend 0.305664668 1.000000000 0.386852990
## durable_investment 0.206323141 0.386852990 1.000000000
## nondurable_investment 0.215640856 0.144158551 0.298216237
## depression 0.009521442 -0.004883243 -0.017430584
## nondurable_investment depression
## sex 0.044284961 -0.007864312
## age -0.015760895 0.104586878
## marital_status -0.012581860 -0.081358216
## children 0.038588415 0.009313072
## household_size 0.041612592 0.002057058
## years_of_edu 0.095695750 -0.126243493
## hh_children 0.142289845 0.004738743
## cons_nondurable 0.193600512 -0.023045708
## asset_durable 0.294971338 -0.047979393
## asset_phone 0.243680181 -0.038934311
## asset_savings 0.648200858 -0.011961091
## asset_land_owned_total 0.040695673 0.010961241
## cons_allfood 0.150219929 -0.023505646
## cons_alcohol -0.010906572 0.042121172
## cons_tobacco 0.011605684 0.007517433
## cons_med_total 0.032056115 0.022115055
## cons_med_children 0.010385155 0.012730428
## cons_ed 0.209248308 0.005230865
## cons_social 0.195687124 -0.017874286
## cons_other 0.223207146 -0.035371066
## ent_nonag_revenue 0.439267596 -0.013235113
## ent_nonag_flowcost 0.784985236 -0.035796973
## ent_total_cost 0.794813756 -0.037822772
## fs_adwholed_often 0.003719725 0.145022197
## fs_chwholed_often -0.037660830 0.066157458
## fs_meat 0.047627091 0.017715394
## fs_enoughtom 0.092933696 -0.020888139
## fs_sleephun -0.004177845 0.017246050
## med_sickdays_hhave -0.033340691 0.060436021
## med_u5_deaths -0.002227480 -0.014339415
## ed_expenses 0.215640856 0.009521442
## ed_schoolattend 0.144158551 -0.004883243
## durable_investment 0.298216237 -0.017430584
## nondurable_investment 1.000000000 -0.035400756
## depression -0.035400756 1.0000000003.2 Explore the data
3.2.1 Box plot and Bar plot.
4.3 Up Sampling
4.4 Down Sampling
5.Model applications and Model Comparison
5.1 imbalanced dataset
5.1.1 Logistic Model
## [1] "Number of rows: 1147"
## [1] "Number of columns: 35"
## [1] "Number of missing values: 0"## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 204 36
## 1 2 1
##
## Accuracy : 0.8436
## 95% CI : (0.7917, 0.8869)
## No Information Rate : 0.8477
## P-Value [Acc > NIR] : 0.6129
##
## Kappa : 0.0278
##
## Mcnemar's Test P-Value : 8.636e-08
##
## Sensitivity : 0.99029
## Specificity : 0.02703
## Pos Pred Value : 0.85000
## Neg Pred Value : 0.33333
## Prevalence : 0.84774
## Detection Rate : 0.83951
## Detection Prevalence : 0.98765
## Balanced Accuracy : 0.50866
##
## 'Positive' Class : 0
## 5.1.1 Summary of Logistic model on imbalanced dataset
This logistic regression model performs well, has a nice accuracy (around 84.36%), but performs poorly in terms of its ability to distinguish between two categories (specifically, the positive category, i.e., 1). The accuracy of the model is similar to the No Information Rate (NIR), which indicates that the model does not significantly outperform random guessing in terms of predictive power. In addition, the model’s sensitivity in the positive category is extremely low and the specificity is very bad.
Accuracy: The accuracy is 84.36%, but this is because the imbalance in the data (most of the data belongs to category 0).
Positive Predictive Value and Negative Predictive Value: PPV is 85%, indicating that when the model predicts a positive category, the probability of being correct is 85%. BUT the NPV is very low which is 33.33%, which means the NP is very low. The model cannot distinguish the class ‘1’.
Sensitivity and Specificity: Sensitivity is as high as 99%, but Specificity is only 2.70%. This indicates that the model hardly recognizes the positive class correctly (CLass=1).
Kappa statistic: The Kappa value is only 0.0278 which indicates that the model has poor predictive power.
Mcnemar’s Test P-value: 8.636e-08, indicating that the model has significant bias in predicting positive and negative classes.
Balanced Accuracy: 50.87%, which further emphasizes the inadequacy of the model in handling unbalanced datasets.
5.1.2 Weighted Logistic model
## [1] "Number of rows: 1147"
## [1] "Number of columns: 35"
## [1] "Number of missing values: 0"## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 108 12
## 1 29 13
##
## Accuracy : 0.7469
## 95% CI : (0.6727, 0.8119)
## No Information Rate : 0.8457
## P-Value [Acc > NIR] : 0.99961
##
## Kappa : 0.2413
##
## Mcnemar's Test P-Value : 0.01246
##
## Sensitivity : 0.7883
## Specificity : 0.5200
## Pos Pred Value : 0.9000
## Neg Pred Value : 0.3095
## Prevalence : 0.8457
## Detection Rate : 0.6667
## Detection Prevalence : 0.7407
## Balanced Accuracy : 0.6542
##
## 'Positive' Class : 0
##
## [1] "AIC: 1238.59469568419"5.1.2 Summary of Weighted Logistic model on imbalanced dataset
Accuracy: 74.69%, which is less than last one.
Predictive Ability: The model has a high prediction accuracy for the positive category (90%) but performs poorly for the negative category (NPV is only 30.95%), indicating that the model is less reliable in predicting the negative category. So this result is the similar to last one because of the imbalanced data.
Balanced Accuracy: 0.6542, indicating that the model is not very well when it encounters imbalanced dataset. Especially encoutner the negative class (class=1).
Mcnemar’s Test P-Value: 0.01246, indicating that the model has high bias when it deal with different classes.
Kappa: 0.2413, indicating that this model is much better than last one. Because this one get the weight into class ‘1’.
5.1.3 Decision Tree model
## Loading required package: tibble## Loading required package: bitops## Rattle: A free graphical interface for data science with R.
## Version 5.5.1 Copyright (c) 2006-2021 Togaware Pty Ltd.
## Type 'rattle()' to shake, rattle, and roll your data.## [1] "Number of rows: 1147"
## [1] "Number of columns: 35"
## [1] "Number of missing values: 0"
## Call:
## rpart(formula = depressed ~ ., data = train_data, method = "class")
## n= 570
##
## CP nsplit rel error xerror xstd
## 1 0.03030303 0 1.0000000 1.000000 0.09802678
## 2 0.02272727 3 0.9090909 1.079545 0.10110870
## 3 0.01136364 5 0.8636364 1.181818 0.10478269
## 4 0.01000000 6 0.8522727 1.261364 0.10743548
##
## Variable importance
## hh_children years_of_edu med_sickdays_hhave
## 14 12 11
## cons_social fs_adwholed_often cons_other
## 10 10 8
## cons_nondurable durable_investment age
## 5 5 4
## cons_allfood nondurable_investment asset_durable
## 4 3 3
## fs_chwholed_often household_size asset_savings
## 3 2 1
## fs_sleephun fs_meat
## 1 1
##
## Node number 1: 570 observations, complexity param=0.03030303
## predicted class=0 expected loss=0.154386 P(node) =1
## class counts: 482 88
## probabilities: 0.846 0.154
## left son=2 (477 obs) right son=3 (93 obs)
## Primary splits:
## years_of_edu < 6.5 to the right, improve=4.107167, (0 missing)
## fs_adwholed_often < 2 to the left, improve=3.973162, (0 missing)
## children < 0.5 to the right, improve=2.285400, (0 missing)
## age < 66.5 to the left, improve=2.021110, (0 missing)
## asset_phone < 15.93529 to the right, improve=1.665369, (0 missing)
## Surrogate splits:
## age < 56.5 to the left, agree=0.870, adj=0.204, (0 split)
## household_size < 1.5 to the right, agree=0.840, adj=0.022, (0 split)
## cons_social < 24.08979 to the left, agree=0.840, adj=0.022, (0 split)
## children < 0.5 to the right, agree=0.839, adj=0.011, (0 split)
## cons_med_children < 12.8123 to the left, agree=0.839, adj=0.011, (0 split)
##
## Node number 2: 477 observations, complexity param=0.02272727
## predicted class=0 expected loss=0.1278826 P(node) =0.8368421
## class counts: 416 61
## probabilities: 0.872 0.128
## left son=4 (253 obs) right son=5 (224 obs)
## Primary splits:
## cons_social < 0.7273647 to the right, improve=1.8047670, (0 missing)
## durable_investment < 234.8594 to the right, improve=1.6072560, (0 missing)
## asset_phone < 63.26071 to the left, improve=1.3022130, (0 missing)
## ed_expenses < 45.6438 to the left, improve=0.8842878, (0 missing)
## fs_adwholed_often < 2 to the left, improve=0.8533597, (0 missing)
## Surrogate splits:
## cons_nondurable < 46.84868 to the right, agree=0.878, adj=0.741, (0 split)
## cons_other < 3.483343 to the right, agree=0.878, adj=0.741, (0 split)
## durable_investment < 36.43497 to the right, agree=0.878, adj=0.741, (0 split)
## nondurable_investment < 0.02780446 to the right, agree=0.878, adj=0.741, (0 split)
## asset_durable < 11.29084 to the right, agree=0.876, adj=0.737, (0 split)
##
## Node number 3: 93 observations, complexity param=0.03030303
## predicted class=0 expected loss=0.2903226 P(node) =0.1631579
## class counts: 66 27
## probabilities: 0.710 0.290
## left son=6 (69 obs) right son=7 (24 obs)
## Primary splits:
## fs_adwholed_often < 2 to the left, improve=4.087073, (0 missing)
## cons_social < 1.621556 to the left, improve=3.937965, (0 missing)
## nondurable_investment < 4.569942 to the left, improve=2.632348, (0 missing)
## cons_alcohol < 0.587257 to the right, improve=2.547581, (0 missing)
## ent_total_cost < 4.771246 to the left, improve=2.439231, (0 missing)
## Surrogate splits:
## fs_chwholed_often < 2 to the left, agree=0.785, adj=0.167, (0 split)
## fs_sleephun < 0.5 to the left, agree=0.774, adj=0.125, (0 split)
## fs_meat < 0.5 to the right, agree=0.763, adj=0.083, (0 split)
## cons_med_total < 1.040999 to the left, agree=0.753, adj=0.042, (0 split)
## cons_ed < 10.2098 to the left, agree=0.753, adj=0.042, (0 split)
##
## Node number 4: 253 observations
## predicted class=0 expected loss=0.08695652 P(node) =0.4438596
## class counts: 231 22
## probabilities: 0.913 0.087
##
## Node number 5: 224 observations, complexity param=0.02272727
## predicted class=0 expected loss=0.1741071 P(node) =0.3929825
## class counts: 185 39
## probabilities: 0.826 0.174
## left son=10 (214 obs) right son=11 (10 obs)
## Primary splits:
## hh_children < 4.5 to the left, improve=5.789736, (0 missing)
## fs_adwholed_often < 2 to the left, improve=4.149148, (0 missing)
## cons_ed < 1.287903 to the left, improve=3.827600, (0 missing)
## ed_expenses < 15.45483 to the left, improve=3.535107, (0 missing)
## cons_med_children < 0.4003842 to the right, improve=2.183618, (0 missing)
## Surrogate splits:
## asset_savings < 28.82767 to the left, agree=0.96, adj=0.1, (0 split)
## fs_chwholed_often < 2 to the left, agree=0.96, adj=0.1, (0 split)
## durable_investment < 843.3353 to the left, agree=0.96, adj=0.1, (0 split)
##
## Node number 6: 69 observations, complexity param=0.01136364
## predicted class=0 expected loss=0.2028986 P(node) =0.1210526
## class counts: 55 14
## probabilities: 0.797 0.203
## left son=12 (62 obs) right son=13 (7 obs)
## Primary splits:
## cons_other < 34.5932 to the left, improve=2.1160760, (0 missing)
## cons_alcohol < 0.587257 to the right, improve=0.9629084, (0 missing)
## children < 1.5 to the left, improve=0.8641367, (0 missing)
## years_of_edu < 5.5 to the right, improve=0.8101365, (0 missing)
## cons_nondurable < 241.4361 to the left, improve=0.7934950, (0 missing)
## Surrogate splits:
## cons_nondurable < 266.7672 to the left, agree=0.928, adj=0.286, (0 split)
## cons_social < 9.142107 to the left, agree=0.928, adj=0.286, (0 split)
## cons_allfood < 215.6241 to the left, agree=0.913, adj=0.143, (0 split)
##
## Node number 7: 24 observations, complexity param=0.03030303
## predicted class=1 expected loss=0.4583333 P(node) =0.04210526
## class counts: 11 13
## probabilities: 0.458 0.542
## left son=14 (14 obs) right son=15 (10 obs)
## Primary splits:
## med_sickdays_hhave < 1.525 to the left, improve=4.402381, (0 missing)
## cons_social < 1.354633 to the left, improve=2.938889, (0 missing)
## ed_schoolattend < 0.8571429 to the right, improve=2.937646, (0 missing)
## years_of_edu < 4.5 to the left, improve=2.288095, (0 missing)
## ent_total_cost < 4.771246 to the left, improve=1.399184, (0 missing)
## Surrogate splits:
## cons_social < 3.203074 to the left, agree=0.750, adj=0.4, (0 split)
## cons_allfood < 32.61111 to the right, agree=0.708, adj=0.3, (0 split)
## age < 66 to the left, agree=0.667, adj=0.2, (0 split)
## household_size < 1.5 to the right, agree=0.667, adj=0.2, (0 split)
## years_of_edu < 3.5 to the left, agree=0.667, adj=0.2, (0 split)
##
## Node number 10: 214 observations
## predicted class=0 expected loss=0.1495327 P(node) =0.3754386
## class counts: 182 32
## probabilities: 0.850 0.150
##
## Node number 11: 10 observations
## predicted class=1 expected loss=0.3 P(node) =0.01754386
## class counts: 3 7
## probabilities: 0.300 0.700
##
## Node number 12: 62 observations
## predicted class=0 expected loss=0.1612903 P(node) =0.1087719
## class counts: 52 10
## probabilities: 0.839 0.161
##
## Node number 13: 7 observations
## predicted class=1 expected loss=0.4285714 P(node) =0.0122807
## class counts: 3 4
## probabilities: 0.429 0.571
##
## Node number 14: 14 observations
## predicted class=0 expected loss=0.2857143 P(node) =0.0245614
## class counts: 10 4
## probabilities: 0.714 0.286
##
## Node number 15: 10 observations
## predicted class=1 expected loss=0.1 P(node) =0.01754386
## class counts: 1 9
## probabilities: 0.100 0.900
##
## n= 570
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 570 88 0 (0.84561404 0.15438596)
## 2) years_of_edu>=6.5 477 61 0 (0.87211740 0.12788260)
## 4) cons_social>=0.7273647 253 22 0 (0.91304348 0.08695652) *
## 5) cons_social< 0.7273647 224 39 0 (0.82589286 0.17410714)
## 10) hh_children< 4.5 214 32 0 (0.85046729 0.14953271) *
## 11) hh_children>=4.5 10 3 1 (0.30000000 0.70000000) *
## 3) years_of_edu< 6.5 93 27 0 (0.70967742 0.29032258)
## 6) fs_adwholed_often< 2 69 14 0 (0.79710145 0.20289855)
## 12) cons_other< 34.5932 62 10 0 (0.83870968 0.16129032) *
## 13) cons_other>=34.5932 7 3 1 (0.42857143 0.57142857) *
## 7) fs_adwholed_often>=2 24 11 1 (0.45833333 0.54166667)
## 14) med_sickdays_hhave< 1.525 14 4 0 (0.71428571 0.28571429) *
## 15) med_sickdays_hhave>=1.525 10 1 1 (0.10000000 0.90000000) *
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 199 36
## 1 7 1
##
## Accuracy : 0.823
## 95% CI : (0.7691, 0.8689)
## No Information Rate : 0.8477
## P-Value [Acc > NIR] : 0.8759
##
## Kappa : -0.0102
##
## Mcnemar's Test P-Value : 1.955e-05
##
## Sensitivity : 0.96602
## Specificity : 0.02703
## Pos Pred Value : 0.84681
## Neg Pred Value : 0.12500
## Prevalence : 0.84774
## Detection Rate : 0.81893
## Detection Prevalence : 0.96708
## Balanced Accuracy : 0.49652
##
## 'Positive' Class : 0
## ## $model
## n= 570
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 570 88 0 (0.84561404 0.15438596)
## 2) years_of_edu>=6.5 477 61 0 (0.87211740 0.12788260)
## 4) cons_social>=0.7273647 253 22 0 (0.91304348 0.08695652) *
## 5) cons_social< 0.7273647 224 39 0 (0.82589286 0.17410714)
## 10) hh_children< 4.5 214 32 0 (0.85046729 0.14953271) *
## 11) hh_children>=4.5 10 3 1 (0.30000000 0.70000000) *
## 3) years_of_edu< 6.5 93 27 0 (0.70967742 0.29032258)
## 6) fs_adwholed_often< 2 69 14 0 (0.79710145 0.20289855)
## 12) cons_other< 34.5932 62 10 0 (0.83870968 0.16129032) *
## 13) cons_other>=34.5932 7 3 1 (0.42857143 0.57142857) *
## 7) fs_adwholed_often>=2 24 11 1 (0.45833333 0.54166667)
## 14) med_sickdays_hhave< 1.525 14 4 0 (0.71428571 0.28571429) *
## 15) med_sickdays_hhave>=1.525 10 1 1 (0.10000000 0.90000000) *
##
## $confusion_matrix
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 199 36
## 1 7 1
##
## Accuracy : 0.823
## 95% CI : (0.7691, 0.8689)
## No Information Rate : 0.8477
## P-Value [Acc > NIR] : 0.8759
##
## Kappa : -0.0102
##
## Mcnemar's Test P-Value : 1.955e-05
##
## Sensitivity : 0.96602
## Specificity : 0.02703
## Pos Pred Value : 0.84681
## Neg Pred Value : 0.12500
## Prevalence : 0.84774
## Detection Rate : 0.81893
## Detection Prevalence : 0.96708
## Balanced Accuracy : 0.49652
##
## 'Positive' Class : 0
## 5.1.3 Summary of Decision Tree model on imbalanced dataset
Based on the decision tree model and confusion matrix data, the model mainly predicted category 0 (non-depressed), but performed poorly for category 1 (depressed).(the similar result as above some models).
Accuracy: 82.3%, the model is highly accurate
Kappa statistic: Kappa is negative, indicating that the model has poor predictive power.
Sensitivity and specificity: the sensitivity was high (96.6%), indicating that the model was able to identify individuals with non-depressive symptoms well; however, the specificity was extremely low (2.7%), indicating that it was almost impossible to correctly identify individuals with true depressive symptoms.
Positive and negative predictive values: the positive predictive value is 84.68%, but the negative predictive value is 12.5%, indicating the model’s poor ability to predict class ‘1’.
5.2 Balanced dataset
5.2.1 Logistic model on balanced dataset (Upsampling)
## [1] "Number of rows: 1147"
## [1] "Number of columns: 35"
## [1] "Number of missing values: 0"## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 142 86
## 1 64 120
##
## Accuracy : 0.6359
## 95% CI : (0.5874, 0.6825)
## No Information Rate : 0.5
## P-Value [Acc > NIR] : 1.884e-08
##
## Kappa : 0.2718
##
## Mcnemar's Test P-Value : 0.08641
##
## Sensitivity : 0.6893
## Specificity : 0.5825
## Pos Pred Value : 0.6228
## Neg Pred Value : 0.6522
## Prevalence : 0.5000
## Detection Rate : 0.3447
## Detection Prevalence : 0.5534
## Balanced Accuracy : 0.6359
##
## 'Positive' Class : 0
## 5.2.1 Summary of Logistic model on balanced dataset
Summarizing the model performance: The overall performance of the model was good with an accuracy of 63.59% . But the predictive ability is relatively relatively good in unbalanced data. But the sensitivity and specificity performance is not good.
No Information Rate (NIR): 0.5, indicating balanced data categories.
P-Value [Acc > NIR]: 1.884e-08. This very small p-value indicates that the model is significantly more accurate than the prediction rate without any information.
Kappa: 0.2718, indicating that the model has some predictive power.
Mcnemar’s Test P-Value: 0.08641. This value is greater than 0.05, indicating that there is no significant bias between predicting positive and negative categories.
Sensitivity: 68.93%. This means that the model correctly identifies 68.93% of the actual positive classes, indicating that the model performs well in identifying actual positive classes.
Specificity: 58.25%. This means that the model correctly identifies 58.25% of the actual negative classes, indicating that the model has improved its performance relative to the previous model.
Pos Pred Value, PPV: 62.28%. This is the percentage of predicted positive categories that are actually positive, indicating that when the model predicts a sample to be positive, there is a 62.28% probability that it will be correct.
Neg Pred Value, NPV: 65.22%. This is the percentage of predicted negative categories that are actually negative, indicating that when the model predicts a sample to be negative, there is a 65.22% probability of being correct.
Balanced Accuracy: 63.59%. This is the average of the sensitivity and specificity. It indicates that the model is equally capable of predicting both categories.
5.2.2 Decision Tree model on balanced dataset (Upsampling)
## [1] "Number of rows: 1147"
## [1] "Number of columns: 35"
## [1] "Number of missing values: 0"
## Call:
## rpart(formula = depressed ~ ., data = train_data, method = "class")
## n= 964
##
## CP nsplit rel error xerror xstd
## 1 0.15560166 0 1.0000000 1.0788382 0.03210758
## 2 0.10788382 1 0.8443983 0.9107884 0.03207941
## 3 0.03941909 2 0.7365145 0.7842324 0.03144917
## 4 0.01867220 3 0.6970954 0.7406639 0.03110591
## 5 0.01659751 5 0.6597510 0.7385892 0.03108789
## 6 0.01556017 8 0.6058091 0.6867220 0.03058654
## 7 0.01452282 15 0.4854772 0.6867220 0.03058654
## 8 0.01244813 16 0.4709544 0.6473029 0.03013808
## 9 0.01175657 17 0.4585062 0.6307054 0.02993114
## 10 0.01000000 20 0.4232365 0.6078838 0.02962849
##
## Variable importance
## cons_social cons_nondurable cons_other
## 10 8 7
## asset_durable cons_allfood cons_med_children
## 6 6 6
## durable_investment fs_chwholed_often med_sickdays_hhave
## 5 5 5
## fs_meat children asset_phone
## 5 4 4
## fs_adwholed_often household_size ent_total_cost
## 4 4 3
## marital_status age nondurable_investment
## 3 3 3
## fs_sleephun years_of_edu cons_alcohol
## 2 2 2
## cons_med_total cons_tobacco asset_savings
## 1 1 1
##
## Node number 1: 964 observations, complexity param=0.1556017
## predicted class=0 expected loss=0.5 P(node) =1
## class counts: 482 482
## probabilities: 0.500 0.500
## left son=2 (755 obs) right son=3 (209 obs)
## Primary splits:
## fs_adwholed_often < 2 to the left, improve=17.18210, (0 missing)
## med_sickdays_hhave < 1.469298 to the left, improve=15.26727, (0 missing)
## cons_social < 3.22643 to the right, improve=14.05538, (0 missing)
## durable_investment < 282.9833 to the right, improve=12.82277, (0 missing)
## years_of_edu < 6.5 to the right, improve=12.75755, (0 missing)
## Surrogate splits:
## fs_sleephun < 0.5 to the left, agree=0.859, adj=0.349, (0 split)
## fs_chwholed_often < 0.9384058 to the left, agree=0.856, adj=0.335, (0 split)
## cons_social < 20.57975 to the left, agree=0.793, adj=0.043, (0 split)
## cons_med_total < 29.62843 to the left, agree=0.789, adj=0.029, (0 split)
## asset_savings < 94.49069 to the left, agree=0.785, adj=0.010, (0 split)
##
## Node number 2: 755 observations, complexity param=0.1078838
## predicted class=0 expected loss=0.4503311 P(node) =0.783195
## class counts: 415 340
## probabilities: 0.550 0.450
## left son=4 (357 obs) right son=5 (398 obs)
## Primary splits:
## cons_social < 0.08007685 to the right, improve=22.26146, (0 missing)
## fs_meat < 3.03444 to the left, improve=21.27456, (0 missing)
## nondurable_investment < 0.3447753 to the right, improve=17.67330, (0 missing)
## ent_total_cost < 0.07785249 to the right, improve=16.71426, (0 missing)
## cons_nondurable < 13.62031 to the right, improve=16.65899, (0 missing)
## Surrogate splits:
## asset_durable < 12.0916 to the right, agree=0.959, adj=0.913, (0 split)
## durable_investment < 20.90006 to the right, agree=0.958, adj=0.910, (0 split)
## cons_nondurable < 13.62031 to the right, agree=0.956, adj=0.908, (0 split)
## cons_allfood < 2.616797 to the right, agree=0.956, adj=0.908, (0 split)
## cons_other < 0.4804611 to the right, agree=0.955, adj=0.905, (0 split)
##
## Node number 3: 209 observations, complexity param=0.01659751
## predicted class=1 expected loss=0.3205742 P(node) =0.216805
## class counts: 67 142
## probabilities: 0.321 0.679
## left son=6 (108 obs) right son=7 (101 obs)
## Primary splits:
## med_sickdays_hhave < 1.775 to the left, improve=10.279040, (0 missing)
## durable_investment < 283.7841 to the right, improve= 8.556608, (0 missing)
## cons_other < 44.05828 to the right, improve= 6.367930, (0 missing)
## ent_total_cost < 0.6517366 to the left, improve= 5.469878, (0 missing)
## years_of_edu < 8.5 to the right, improve= 4.869325, (0 missing)
## Surrogate splits:
## cons_social < 2.462363 to the left, agree=0.646, adj=0.267, (0 split)
## cons_med_total < 14.01345 to the left, agree=0.622, adj=0.218, (0 split)
## cons_med_children < 0.8808453 to the left, agree=0.622, adj=0.218, (0 split)
## marital_status < 0.5 to the right, agree=0.617, adj=0.208, (0 split)
## nondurable_investment < 40.25419 to the left, agree=0.612, adj=0.198, (0 split)
##
## Node number 4: 357 observations, complexity param=0.03941909
## predicted class=0 expected loss=0.3221289 P(node) =0.370332
## class counts: 242 115
## probabilities: 0.678 0.322
## left son=8 (284 obs) right son=9 (73 obs)
## Primary splits:
## asset_phone < 63.26071 to the left, improve=17.411140, (0 missing)
## fs_meat < 4.5 to the left, improve=10.299610, (0 missing)
## asset_land_owned_total < 1.3 to the right, improve= 8.888106, (0 missing)
## asset_durable < 523.8868 to the left, improve= 7.820506, (0 missing)
## cons_med_total < 12.33183 to the left, improve= 6.885786, (0 missing)
## Surrogate splits:
## cons_med_children < 10.57014 to the left, agree=0.821, adj=0.123, (0 split)
## asset_durable < 584.561 to the left, agree=0.812, adj=0.082, (0 split)
## nondurable_investment < 0.3447753 to the right, agree=0.812, adj=0.082, (0 split)
## cons_nondurable < 423.3387 to the left, agree=0.810, adj=0.068, (0 split)
## cons_other < 77.35424 to the left, agree=0.810, adj=0.068, (0 split)
##
## Node number 5: 398 observations, complexity param=0.01556017
## predicted class=1 expected loss=0.4346734 P(node) =0.4128631
## class counts: 173 225
## probabilities: 0.435 0.565
## left son=10 (312 obs) right son=11 (86 obs)
## Primary splits:
## fs_chwholed_often < 0.112069 to the right, improve=8.963033, (0 missing)
## children < 0.5 to the right, improve=7.398128, (0 missing)
## cons_med_children < 0.6780793 to the right, improve=7.359677, (0 missing)
## marital_status < 0.5 to the right, improve=7.297268, (0 missing)
## med_sickdays_hhave < 3.75 to the left, improve=5.508631, (0 missing)
## Surrogate splits:
## cons_med_children < 0.1501441 to the right, agree=0.987, adj=0.942, (0 split)
## children < 0.5 to the right, agree=0.925, adj=0.651, (0 split)
## household_size < 2.5 to the right, agree=0.894, adj=0.512, (0 split)
## cons_nondurable < 14.34405 to the left, agree=0.862, adj=0.360, (0 split)
## asset_durable < 2.882766 to the left, agree=0.862, adj=0.360, (0 split)
##
## Node number 6: 108 observations, complexity param=0.01659751
## predicted class=1 expected loss=0.4722222 P(node) =0.1120332
## class counts: 51 57
## probabilities: 0.472 0.528
## left son=12 (16 obs) right son=13 (92 obs)
## Primary splits:
## cons_social < 4.170669 to the right, improve=10.463770, (0 missing)
## marital_status < 0.5 to the left, improve= 8.233333, (0 missing)
## ent_total_cost < 0.8713918 to the left, improve= 7.724959, (0 missing)
## fs_meat < 3.5 to the right, improve= 6.699595, (0 missing)
## asset_durable < 61.01856 to the right, improve= 6.519048, (0 missing)
## Surrogate splits:
## cons_med_children < 2.001921 to the right, agree=0.880, adj=0.188, (0 split)
## cons_other < 44.37859 to the right, agree=0.880, adj=0.188, (0 split)
## med_sickdays_hhave < 1.669643 to the right, agree=0.880, adj=0.188, (0 split)
## cons_med_total < 2.322229 to the right, agree=0.870, adj=0.125, (0 split)
## years_of_edu < 11 to the right, agree=0.861, adj=0.063, (0 split)
##
## Node number 7: 101 observations
## predicted class=1 expected loss=0.1584158 P(node) =0.1047718
## class counts: 16 85
## probabilities: 0.158 0.842
##
## Node number 8: 284 observations, complexity param=0.01175657
## predicted class=0 expected loss=0.2429577 P(node) =0.2946058
## class counts: 215 69
## probabilities: 0.757 0.243
## left son=16 (117 obs) right son=17 (167 obs)
## Primary splits:
## ent_total_cost < 3.359891 to the left, improve=8.827632, (0 missing)
## nondurable_investment < 3.705779 to the left, improve=8.730911, (0 missing)
## ent_nonag_revenue < 333.1197 to the left, improve=5.414585, (0 missing)
## ed_expenses < 15.61499 to the left, improve=5.241596, (0 missing)
## years_of_edu < 5.5 to the right, improve=5.046073, (0 missing)
## Surrogate splits:
## nondurable_investment < 7.223599 to the left, agree=0.866, adj=0.675, (0 split)
## cons_nondurable < 129.3255 to the left, agree=0.683, adj=0.231, (0 split)
## cons_other < 13.70115 to the left, agree=0.662, adj=0.179, (0 split)
## durable_investment < 140.7668 to the left, agree=0.651, adj=0.154, (0 split)
## cons_allfood < 85.47331 to the left, agree=0.648, adj=0.145, (0 split)
##
## Node number 9: 73 observations, complexity param=0.0186722
## predicted class=1 expected loss=0.369863 P(node) =0.07572614
## class counts: 27 46
## probabilities: 0.370 0.630
## left son=18 (29 obs) right son=19 (44 obs)
## Primary splits:
## fs_meat < 3.5 to the left, improve=7.833040, (0 missing)
## cons_social < 3.269805 to the right, improve=6.299506, (0 missing)
## fs_sleephun < 0.5 to the right, improve=4.150348, (0 missing)
## age < 29.5 to the right, improve=4.109722, (0 missing)
## years_of_edu < 9.5 to the left, improve=3.661097, (0 missing)
## Surrogate splits:
## cons_other < 24.34336 to the left, agree=0.836, adj=0.586, (0 split)
## fs_sleephun < 0.5 to the right, agree=0.767, adj=0.414, (0 split)
## cons_allfood < 137.5272 to the left, agree=0.753, adj=0.379, (0 split)
## cons_nondurable < 92.18123 to the left, agree=0.740, adj=0.345, (0 split)
## asset_savings < 3.203074 to the left, agree=0.726, adj=0.310, (0 split)
##
## Node number 10: 312 observations, complexity param=0.01556017
## predicted class=1 expected loss=0.4903846 P(node) =0.3236515
## class counts: 153 159
## probabilities: 0.490 0.510
## left son=20 (10 obs) right son=21 (302 obs)
## Primary splits:
## household_size < 2.5 to the left, improve=5.366149, (0 missing)
## children < 1.5 to the left, improve=4.720085, (0 missing)
## age < 22.5 to the left, improve=3.436915, (0 missing)
## marital_status < 0.5 to the right, improve=2.763880, (0 missing)
## cons_med_children < 1.525836 to the right, improve=2.550214, (0 missing)
##
## Node number 11: 86 observations
## predicted class=1 expected loss=0.2325581 P(node) =0.08921162
## class counts: 20 66
## probabilities: 0.233 0.767
##
## Node number 12: 16 observations
## predicted class=0 expected loss=0 P(node) =0.01659751
## class counts: 16 0
## probabilities: 1.000 0.000
##
## Node number 13: 92 observations, complexity param=0.01659751
## predicted class=1 expected loss=0.3804348 P(node) =0.09543568
## class counts: 35 57
## probabilities: 0.380 0.620
## left son=26 (10 obs) right son=27 (82 obs)
## Primary splits:
## marital_status < 0.5 to the left, improve=8.613468, (0 missing)
## cons_allfood < 65.76883 to the left, improve=7.987229, (0 missing)
## ent_total_cost < 0.8713918 to the left, improve=6.309825, (0 missing)
## age < 50 to the right, improve=5.816624, (0 missing)
## nondurable_investment < 1.782266 to the left, improve=5.816624, (0 missing)
## Surrogate splits:
## age < 53 to the right, agree=0.935, adj=0.4, (0 split)
## asset_land_owned_total < 2.495 to the right, agree=0.913, adj=0.2, (0 split)
##
## Node number 16: 117 observations
## predicted class=0 expected loss=0.09401709 P(node) =0.1213693
## class counts: 106 11
## probabilities: 0.906 0.094
##
## Node number 17: 167 observations, complexity param=0.01175657
## predicted class=0 expected loss=0.3473054 P(node) =0.1732365
## class counts: 109 58
## probabilities: 0.653 0.347
## left son=34 (125 obs) right son=35 (42 obs)
## Primary splits:
## years_of_edu < 7.5 to the right, improve=6.898480, (0 missing)
## cons_nondurable < 53.34834 to the right, improve=5.580367, (0 missing)
## durable_investment < 191.5102 to the right, improve=4.503051, (0 missing)
## ent_total_cost < 16.04206 to the right, improve=4.358415, (0 missing)
## asset_phone < 41.63996 to the right, improve=4.268866, (0 missing)
## Surrogate splits:
## cons_nondurable < 66.13776 to the right, agree=0.802, adj=0.214, (0 split)
## cons_allfood < 38.47273 to the right, agree=0.802, adj=0.214, (0 split)
## age < 42 to the left, agree=0.796, adj=0.190, (0 split)
## cons_tobacco < 1.014088 to the left, agree=0.790, adj=0.167, (0 split)
## durable_investment < 100.6285 to the right, agree=0.784, adj=0.143, (0 split)
##
## Node number 18: 29 observations, complexity param=0.0186722
## predicted class=0 expected loss=0.3448276 P(node) =0.03008299
## class counts: 19 10
## probabilities: 0.655 0.345
## left son=36 (18 obs) right son=37 (11 obs)
## Primary splits:
## fs_meat < 1.5 to the right, improve=11.285270, (0 missing)
## cons_social < 2.602498 to the right, improve= 6.436782, (0 missing)
## cons_other < 20.54772 to the right, improve= 5.603448, (0 missing)
## ed_expenses < 20.65983 to the left, improve= 4.214559, (0 missing)
## asset_durable < 251.7616 to the right, improve= 3.629764, (0 missing)
## Surrogate splits:
## cons_social < 2.602498 to the right, agree=0.862, adj=0.636, (0 split)
## cons_nondurable < 84.25133 to the right, agree=0.759, adj=0.364, (0 split)
## asset_durable < 153.0269 to the right, agree=0.759, adj=0.364, (0 split)
## cons_other < 20.54772 to the right, agree=0.759, adj=0.364, (0 split)
## med_sickdays_hhave < 3.925 to the left, agree=0.759, adj=0.364, (0 split)
##
## Node number 19: 44 observations
## predicted class=1 expected loss=0.1818182 P(node) =0.04564315
## class counts: 8 36
## probabilities: 0.182 0.818
##
## Node number 20: 10 observations
## predicted class=0 expected loss=0 P(node) =0.01037344
## class counts: 10 0
## probabilities: 1.000 0.000
##
## Node number 21: 302 observations, complexity param=0.01556017
## predicted class=1 expected loss=0.4735099 P(node) =0.313278
## class counts: 143 159
## probabilities: 0.474 0.526
## left son=42 (244 obs) right son=43 (58 obs)
## Primary splits:
## marital_status < 0.5 to the right, improve=4.672824, (0 missing)
## age < 22.5 to the left, improve=2.490137, (0 missing)
## children < 6.5 to the left, improve=2.361525, (0 missing)
## fs_chwholed_often < 0.4395492 to the right, improve=1.611502, (0 missing)
## years_of_edu < 7.5 to the right, improve=1.274011, (0 missing)
## Surrogate splits:
## years_of_edu < 5.5 to the right, agree=0.821, adj=0.069, (0 split)
##
## Node number 26: 10 observations
## predicted class=0 expected loss=0 P(node) =0.01037344
## class counts: 10 0
## probabilities: 1.000 0.000
##
## Node number 27: 82 observations, complexity param=0.01452282
## predicted class=1 expected loss=0.304878 P(node) =0.08506224
## class counts: 25 57
## probabilities: 0.305 0.695
## left son=54 (13 obs) right son=55 (69 obs)
## Primary splits:
## ent_total_cost < 0.8713918 to the left, improve=6.662452, (0 missing)
## cons_allfood < 65.76883 to the left, improve=5.572647, (0 missing)
## cons_social < 1.000961 to the right, improve=4.943337, (0 missing)
## cons_nondurable < 73.02399 to the left, improve=3.715162, (0 missing)
## asset_durable < 61.01856 to the right, improve=3.637501, (0 missing)
## Surrogate splits:
## nondurable_investment < 2.008594 to the left, agree=0.927, adj=0.538, (0 split)
## cons_nondurable < 41.84797 to the left, agree=0.890, adj=0.308, (0 split)
## fs_meat < 0.5 to the left, agree=0.878, adj=0.231, (0 split)
##
## Node number 34: 125 observations
## predicted class=0 expected loss=0.264 P(node) =0.129668
## class counts: 92 33
## probabilities: 0.736 0.264
##
## Node number 35: 42 observations, complexity param=0.01175657
## predicted class=1 expected loss=0.4047619 P(node) =0.04356846
## class counts: 17 25
## probabilities: 0.405 0.595
## left son=70 (9 obs) right son=71 (33 obs)
## Primary splits:
## cons_alcohol < 0.587257 to the right, improve=8.116883, (0 missing)
## ent_total_cost < 10.20757 to the right, improve=5.418873, (0 missing)
## cons_ed < 2.335575 to the left, improve=4.132326, (0 missing)
## cons_tobacco < 0.6978126 to the right, improve=4.004762, (0 missing)
## ed_expenses < 31.87059 to the left, improve=3.569903, (0 missing)
## Surrogate splits:
## cons_tobacco < 0.6978126 to the right, agree=0.833, adj=0.222, (0 split)
## cons_ed < 0.6673071 to the left, agree=0.833, adj=0.222, (0 split)
## med_sickdays_hhave < 4.45 to the right, agree=0.833, adj=0.222, (0 split)
## ed_expenses < 8.007685 to the left, agree=0.833, adj=0.222, (0 split)
## durable_investment < 84.29773 to the left, agree=0.833, adj=0.222, (0 split)
##
## Node number 36: 18 observations
## predicted class=0 expected loss=0 P(node) =0.0186722
## class counts: 18 0
## probabilities: 1.000 0.000
##
## Node number 37: 11 observations
## predicted class=1 expected loss=0.09090909 P(node) =0.01141079
## class counts: 1 10
## probabilities: 0.091 0.909
##
## Node number 42: 244 observations, complexity param=0.01556017
## predicted class=0 expected loss=0.4836066 P(node) =0.253112
## class counts: 126 118
## probabilities: 0.516 0.484
## left son=84 (212 obs) right son=85 (32 obs)
## Primary splits:
## children < 5.5 to the left, improve=3.062249, (0 missing)
## age < 24.5 to the left, improve=2.760817, (0 missing)
## fs_chwholed_often < 0.4395492 to the right, improve=2.287265, (0 missing)
## years_of_edu < 4.5 to the left, improve=2.127327, (0 missing)
## cons_med_children < 2.100913 to the right, improve=1.663826, (0 missing)
## Surrogate splits:
## cons_med_children < 1.136585 to the right, agree=0.963, adj=0.719, (0 split)
## household_size < 7.5 to the left, agree=0.947, adj=0.594, (0 split)
## med_sickdays_hhave < 1.295687 to the right, agree=0.947, adj=0.594, (0 split)
## fs_chwholed_often < 0.5664414 to the left, agree=0.881, adj=0.094, (0 split)
##
## Node number 43: 58 observations
## predicted class=1 expected loss=0.2931034 P(node) =0.06016598
## class counts: 17 41
## probabilities: 0.293 0.707
##
## Node number 54: 13 observations
## predicted class=0 expected loss=0.2307692 P(node) =0.01348548
## class counts: 10 3
## probabilities: 0.769 0.231
##
## Node number 55: 69 observations
## predicted class=1 expected loss=0.2173913 P(node) =0.07157676
## class counts: 15 54
## probabilities: 0.217 0.783
##
## Node number 70: 9 observations
## predicted class=0 expected loss=0 P(node) =0.0093361
## class counts: 9 0
## probabilities: 1.000 0.000
##
## Node number 71: 33 observations
## predicted class=1 expected loss=0.2424242 P(node) =0.03423237
## class counts: 8 25
## probabilities: 0.242 0.758
##
## Node number 84: 212 observations, complexity param=0.01556017
## predicted class=0 expected loss=0.4528302 P(node) =0.219917
## class counts: 116 96
## probabilities: 0.547 0.453
## left son=168 (56 obs) right son=169 (156 obs)
## Primary splits:
## household_size < 5.5 to the right, improve=3.390853, (0 missing)
## fs_chwholed_often < 0.4288448 to the right, improve=3.227228, (0 missing)
## years_of_edu < 13.5 to the right, improve=2.968799, (0 missing)
## med_sickdays_hhave < 1.525668 to the left, improve=2.657614, (0 missing)
## age < 31.5 to the right, improve=2.086907, (0 missing)
## Surrogate splits:
## children < 3.5 to the right, agree=0.934, adj=0.750, (0 split)
## med_sickdays_hhave < 1.525668 to the left, agree=0.906, adj=0.643, (0 split)
## fs_chwholed_often < 0.4288448 to the right, agree=0.877, adj=0.536, (0 split)
## cons_med_children < 1.238365 to the left, agree=0.858, adj=0.464, (0 split)
## age < 38.5 to the right, agree=0.811, adj=0.286, (0 split)
##
## Node number 85: 32 observations
## predicted class=1 expected loss=0.3125 P(node) =0.03319502
## class counts: 10 22
## probabilities: 0.312 0.688
##
## Node number 168: 56 observations
## predicted class=0 expected loss=0.3035714 P(node) =0.05809129
## class counts: 39 17
## probabilities: 0.696 0.304
##
## Node number 169: 156 observations, complexity param=0.01556017
## predicted class=1 expected loss=0.4935897 P(node) =0.1618257
## class counts: 77 79
## probabilities: 0.494 0.506
## left son=338 (69 obs) right son=339 (87 obs)
## Primary splits:
## age < 24.5 to the left, improve=4.1560950, (0 missing)
## children < 1.5 to the left, improve=3.0010680, (0 missing)
## cons_med_children < 2.100913 to the right, improve=3.0010680, (0 missing)
## fs_chwholed_often < 0.526824 to the right, improve=3.0010680, (0 missing)
## years_of_edu < 11.5 to the left, improve=0.8312297, (0 missing)
## Surrogate splits:
## household_size < 4.5 to the left, agree=0.628, adj=0.159, (0 split)
## med_sickdays_hhave < 1.6844 to the right, agree=0.628, adj=0.159, (0 split)
## years_of_edu < 8.5 to the left, agree=0.622, adj=0.145, (0 split)
## children < 3.5 to the right, agree=0.583, adj=0.058, (0 split)
## cons_med_children < 1.238365 to the left, agree=0.583, adj=0.058, (0 split)
##
## Node number 338: 69 observations, complexity param=0.01244813
## predicted class=0 expected loss=0.3768116 P(node) =0.07157676
## class counts: 43 26
## probabilities: 0.623 0.377
## left son=676 (55 obs) right son=677 (14 obs)
## Primary splits:
## age < 17.5 to the right, improve=4.0006020, (0 missing)
## years_of_edu < 8.5 to the right, improve=2.4492750, (0 missing)
## med_sickdays_hhave < 1.6844 to the left, improve=1.7536230, (0 missing)
## household_size < 4.5 to the right, improve=1.7536230, (0 missing)
## fs_chwholed_often < 0.4288448 to the left, improve=0.7443551, (0 missing)
## Surrogate splits:
## children < 3.5 to the left, agree=0.855, adj=0.286, (0 split)
## cons_med_children < 1.238365 to the right, agree=0.855, adj=0.286, (0 split)
## household_size < 3.5 to the right, agree=0.826, adj=0.143, (0 split)
## med_sickdays_hhave < 2.125778 to the left, agree=0.826, adj=0.143, (0 split)
##
## Node number 339: 87 observations, complexity param=0.01556017
## predicted class=1 expected loss=0.3908046 P(node) =0.09024896
## class counts: 34 53
## probabilities: 0.391 0.609
## left son=678 (9 obs) right son=679 (78 obs)
## Primary splits:
## fs_chwholed_often < 0.4288448 to the right, improve=7.450928, (0 missing)
## children < 1.5 to the left, improve=5.650287, (0 missing)
## cons_med_children < 2.100913 to the right, improve=5.650287, (0 missing)
## age < 32 to the right, improve=3.321839, (0 missing)
## years_of_edu < 12.5 to the right, improve=1.088692, (0 missing)
## Surrogate splits:
## children < 1.5 to the left, agree=0.977, adj=0.778, (0 split)
## cons_med_children < 2.100913 to the right, agree=0.977, adj=0.778, (0 split)
##
## Node number 676: 55 observations
## predicted class=0 expected loss=0.2909091 P(node) =0.05705394
## class counts: 39 16
## probabilities: 0.709 0.291
##
## Node number 677: 14 observations
## predicted class=1 expected loss=0.2857143 P(node) =0.01452282
## class counts: 4 10
## probabilities: 0.286 0.714
##
## Node number 678: 9 observations
## predicted class=0 expected loss=0 P(node) =0.0093361
## class counts: 9 0
## probabilities: 1.000 0.000
##
## Node number 679: 78 observations
## predicted class=1 expected loss=0.3205128 P(node) =0.08091286
## class counts: 25 53
## probabilities: 0.321 0.679
##
## n= 964
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 964 482 0 (0.50000000 0.50000000)
## 2) fs_adwholed_often< 2 755 340 0 (0.54966887 0.45033113)
## 4) cons_social>=0.08007685 357 115 0 (0.67787115 0.32212885)
## 8) asset_phone< 63.26071 284 69 0 (0.75704225 0.24295775)
## 16) ent_total_cost< 3.359891 117 11 0 (0.90598291 0.09401709) *
## 17) ent_total_cost>=3.359891 167 58 0 (0.65269461 0.34730539)
## 34) years_of_edu>=7.5 125 33 0 (0.73600000 0.26400000) *
## 35) years_of_edu< 7.5 42 17 1 (0.40476190 0.59523810)
## 70) cons_alcohol>=0.587257 9 0 0 (1.00000000 0.00000000) *
## 71) cons_alcohol< 0.587257 33 8 1 (0.24242424 0.75757576) *
## 9) asset_phone>=63.26071 73 27 1 (0.36986301 0.63013699)
## 18) fs_meat< 3.5 29 10 0 (0.65517241 0.34482759)
## 36) fs_meat>=1.5 18 0 0 (1.00000000 0.00000000) *
## 37) fs_meat< 1.5 11 1 1 (0.09090909 0.90909091) *
## 19) fs_meat>=3.5 44 8 1 (0.18181818 0.81818182) *
## 5) cons_social< 0.08007685 398 173 1 (0.43467337 0.56532663)
## 10) fs_chwholed_often>=0.112069 312 153 1 (0.49038462 0.50961538)
## 20) household_size< 2.5 10 0 0 (1.00000000 0.00000000) *
## 21) household_size>=2.5 302 143 1 (0.47350993 0.52649007)
## 42) marital_status>=0.5 244 118 0 (0.51639344 0.48360656)
## 84) children< 5.5 212 96 0 (0.54716981 0.45283019)
## 168) household_size>=5.5 56 17 0 (0.69642857 0.30357143) *
## 169) household_size< 5.5 156 77 1 (0.49358974 0.50641026)
## 338) age< 24.5 69 26 0 (0.62318841 0.37681159)
## 676) age>=17.5 55 16 0 (0.70909091 0.29090909) *
## 677) age< 17.5 14 4 1 (0.28571429 0.71428571) *
## 339) age>=24.5 87 34 1 (0.39080460 0.60919540)
## 678) fs_chwholed_often>=0.4288448 9 0 0 (1.00000000 0.00000000) *
## 679) fs_chwholed_often< 0.4288448 78 25 1 (0.32051282 0.67948718) *
## 85) children>=5.5 32 10 1 (0.31250000 0.68750000) *
## 43) marital_status< 0.5 58 17 1 (0.29310345 0.70689655) *
## 11) fs_chwholed_often< 0.112069 86 20 1 (0.23255814 0.76744186) *
## 3) fs_adwholed_often>=2 209 67 1 (0.32057416 0.67942584)
## 6) med_sickdays_hhave< 1.775 108 51 1 (0.47222222 0.52777778)
## 12) cons_social>=4.170669 16 0 0 (1.00000000 0.00000000) *
## 13) cons_social< 4.170669 92 35 1 (0.38043478 0.61956522)
## 26) marital_status< 0.5 10 0 0 (1.00000000 0.00000000) *
## 27) marital_status>=0.5 82 25 1 (0.30487805 0.69512195)
## 54) ent_total_cost< 0.8713918 13 3 0 (0.76923077 0.23076923) *
## 55) ent_total_cost>=0.8713918 69 15 1 (0.21739130 0.78260870) *
## 7) med_sickdays_hhave>=1.775 101 16 1 (0.15841584 0.84158416) *
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 138 52
## 1 68 154
##
## Accuracy : 0.7087
## 95% CI : (0.6623, 0.7522)
## No Information Rate : 0.5
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.4175
##
## Mcnemar's Test P-Value : 0.1709
##
## Sensitivity : 0.6699
## Specificity : 0.7476
## Pos Pred Value : 0.7263
## Neg Pred Value : 0.6937
## Prevalence : 0.5000
## Detection Rate : 0.3350
## Detection Prevalence : 0.4612
## Balanced Accuracy : 0.7087
##
## 'Positive' Class : 0
## ## $model
## n= 964
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 964 482 0 (0.50000000 0.50000000)
## 2) fs_adwholed_often< 2 755 340 0 (0.54966887 0.45033113)
## 4) cons_social>=0.08007685 357 115 0 (0.67787115 0.32212885)
## 8) asset_phone< 63.26071 284 69 0 (0.75704225 0.24295775)
## 16) ent_total_cost< 3.359891 117 11 0 (0.90598291 0.09401709) *
## 17) ent_total_cost>=3.359891 167 58 0 (0.65269461 0.34730539)
## 34) years_of_edu>=7.5 125 33 0 (0.73600000 0.26400000) *
## 35) years_of_edu< 7.5 42 17 1 (0.40476190 0.59523810)
## 70) cons_alcohol>=0.587257 9 0 0 (1.00000000 0.00000000) *
## 71) cons_alcohol< 0.587257 33 8 1 (0.24242424 0.75757576) *
## 9) asset_phone>=63.26071 73 27 1 (0.36986301 0.63013699)
## 18) fs_meat< 3.5 29 10 0 (0.65517241 0.34482759)
## 36) fs_meat>=1.5 18 0 0 (1.00000000 0.00000000) *
## 37) fs_meat< 1.5 11 1 1 (0.09090909 0.90909091) *
## 19) fs_meat>=3.5 44 8 1 (0.18181818 0.81818182) *
## 5) cons_social< 0.08007685 398 173 1 (0.43467337 0.56532663)
## 10) fs_chwholed_often>=0.112069 312 153 1 (0.49038462 0.50961538)
## 20) household_size< 2.5 10 0 0 (1.00000000 0.00000000) *
## 21) household_size>=2.5 302 143 1 (0.47350993 0.52649007)
## 42) marital_status>=0.5 244 118 0 (0.51639344 0.48360656)
## 84) children< 5.5 212 96 0 (0.54716981 0.45283019)
## 168) household_size>=5.5 56 17 0 (0.69642857 0.30357143) *
## 169) household_size< 5.5 156 77 1 (0.49358974 0.50641026)
## 338) age< 24.5 69 26 0 (0.62318841 0.37681159)
## 676) age>=17.5 55 16 0 (0.70909091 0.29090909) *
## 677) age< 17.5 14 4 1 (0.28571429 0.71428571) *
## 339) age>=24.5 87 34 1 (0.39080460 0.60919540)
## 678) fs_chwholed_often>=0.4288448 9 0 0 (1.00000000 0.00000000) *
## 679) fs_chwholed_often< 0.4288448 78 25 1 (0.32051282 0.67948718) *
## 85) children>=5.5 32 10 1 (0.31250000 0.68750000) *
## 43) marital_status< 0.5 58 17 1 (0.29310345 0.70689655) *
## 11) fs_chwholed_often< 0.112069 86 20 1 (0.23255814 0.76744186) *
## 3) fs_adwholed_often>=2 209 67 1 (0.32057416 0.67942584)
## 6) med_sickdays_hhave< 1.775 108 51 1 (0.47222222 0.52777778)
## 12) cons_social>=4.170669 16 0 0 (1.00000000 0.00000000) *
## 13) cons_social< 4.170669 92 35 1 (0.38043478 0.61956522)
## 26) marital_status< 0.5 10 0 0 (1.00000000 0.00000000) *
## 27) marital_status>=0.5 82 25 1 (0.30487805 0.69512195)
## 54) ent_total_cost< 0.8713918 13 3 0 (0.76923077 0.23076923) *
## 55) ent_total_cost>=0.8713918 69 15 1 (0.21739130 0.78260870) *
## 7) med_sickdays_hhave>=1.775 101 16 1 (0.15841584 0.84158416) *
##
## $confusion_matrix
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 138 52
## 1 68 154
##
## Accuracy : 0.7087
## 95% CI : (0.6623, 0.7522)
## No Information Rate : 0.5
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.4175
##
## Mcnemar's Test P-Value : 0.1709
##
## Sensitivity : 0.6699
## Specificity : 0.7476
## Pos Pred Value : 0.7263
## Neg Pred Value : 0.6937
## Prevalence : 0.5000
## Detection Rate : 0.3350
## Detection Prevalence : 0.4612
## Balanced Accuracy : 0.7087
##
## 'Positive' Class : 0
## 5.2.2 Summary of Decision Tree model on balanced dataset (Upsampling)
Summarize the model performance: The results show an accuracy of 70.87%, which indicates that the model performs well in distinguishing between the two categories (depressed and non-depressed).The Kappa statistic is 0.4175, which indicates that the model’s predictive power is relatively good. The model showed some validity when dealing with a balanced dataset.
kappa: 0.4175. kappa values between 0.4 and 0.6 indicate that the model has moderate predictive consistency.
Mcnemar’s Test P-Value: 0.1709, which is higher than 0.05, indicating that the difference between the predictions of the positive and negative categories is not statistically significant, and the model is more balanced in predicting the two categories.
Sensitivity: 66.99%. Indicates that the model correctly identifies approximately 67% of non-depressed instances.
Specificity: 74.76%. Indicates that the model correctly identifies approximately 75% of the instances of depression.
Balanced Accuracy: 70.87%. Indicates that the model has excellent performance in handling both categories.
Variable Importance and Split of the Model
5.3.1 Logistic model on balanced dataset (down sampling)
## [1] "Number of rows: 1147"
## [1] "Number of columns: 35"
## [1] "Number of missing values: 0"## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 20 15
## 1 17 22
##
## Accuracy : 0.5676
## 95% CI : (0.4472, 0.6823)
## No Information Rate : 0.5
## P-Value [Acc > NIR] : 0.1477
##
## Kappa : 0.1351
##
## Mcnemar's Test P-Value : 0.8597
##
## Sensitivity : 0.5405
## Specificity : 0.5946
## Pos Pred Value : 0.5714
## Neg Pred Value : 0.5641
## Prevalence : 0.5000
## Detection Rate : 0.2703
## Detection Prevalence : 0.4730
## Balanced Accuracy : 0.5676
##
## 'Positive' Class : 0
## 5.3.1 Summary of Logistic model on balanced dataset (down sampling)
Summarizing the model performance
This logistic regression model performed mediocrely when dealing with a balanced dataset with an accuracy of 56.76%. This indicates that the model is not very effective in distinguishing between depressed and non-depressed states.The Kappa statistic of 0.1351 indicates that the model has average predictive power.
Accuracy: 56.76%. The overall accuracy of the model is low, indicating its limited discriminatory power.
95% CI (Confidence Interval): (44.72%, 68.23%). Confidence intervals are wide, indicating that estimates of model accuracy are not stable enough.
No Information Rate (NIR): 50%. Indicates that if the model does not have any valid information, the prediction accuracy is 50%.
Kappa: 0.1351. This value indicates that the predictive power of the model is not good.
Mcnemar’s Test P-Value: 0.8597, which indicates that the bias between positive and negative predictions is not significant, i.e., the model’s imbalance between the predictions of the two categories is not significant.
Sensitivity and Specificity:54.05% and 59.46%. These two indicators show that the model is weak in recognizing both positive and negative categories.
Positive Predictive Value, PPV and Negative Predictive Value, NPV: PPV is 57.14% and NPV is 56.41%, which indicates that the model is average in predicting correctness.
Balanced Accuracy: 56.76%, which indicates that the model is average in positive and negative class prediction.
5.3.2 Decision Tree model on balanced dataset (down sampling)
## [1] "Number of rows: 1147"
## [1] "Number of columns: 35"
## [1] "Number of missing values: 0"
## Call:
## rpart(formula = depressed ~ ., data = train_data, method = "class")
## n= 176
##
## CP nsplit rel error xerror xstd
## 1 0.23863636 0 1.0000000 1.2045455 0.07378413
## 2 0.05113636 1 0.7613636 0.7954545 0.07378413
## 3 0.03409091 4 0.6022727 0.8863636 0.07488957
## 4 0.02272727 6 0.5340909 0.9204545 0.07513898
## 5 0.01136364 7 0.5113636 0.9090909 0.07506571
## 6 0.01000000 8 0.5000000 0.9090909 0.07506571
##
## Variable importance
## years_of_edu med_sickdays_hhave ed_expenses
## 14 13 9
## cons_ed cons_social nondurable_investment
## 9 7 6
## age household_size children
## 5 4 4
## cons_nondurable cons_allfood hh_children
## 4 4 4
## durable_investment ent_total_cost cons_med_children
## 3 3 3
## cons_other ed_schoolattend fs_chwholed_often
## 3 3 2
## fs_adwholed_often cons_alcohol
## 1 1
##
## Node number 1: 176 observations, complexity param=0.2386364
## predicted class=0 expected loss=0.5 P(node) =1
## class counts: 88 88
## probabilities: 0.500 0.500
## left son=2 (141 obs) right son=3 (35 obs)
## Primary splits:
## years_of_edu < 6.5 to the right, improve=7.863830, (0 missing)
## med_sickdays_hhave < 0.08333333 to the left, improve=6.731935, (0 missing)
## ed_expenses < 51.20914 to the left, improve=3.927273, (0 missing)
## cons_allfood < 186.4439 to the left, improve=3.880071, (0 missing)
## cons_social < 3.269805 to the right, improve=3.705783, (0 missing)
## Surrogate splits:
## age < 46.5 to the left, agree=0.847, adj=0.229, (0 split)
## household_size < 1.5 to the right, agree=0.841, adj=0.200, (0 split)
## children < 0.5 to the right, agree=0.830, adj=0.143, (0 split)
## med_sickdays_hhave < 6.955645 to the left, agree=0.830, adj=0.143, (0 split)
## fs_adwholed_often < 5.25 to the left, agree=0.812, adj=0.057, (0 split)
##
## Node number 2: 141 observations, complexity param=0.05113636
## predicted class=0 expected loss=0.4255319 P(node) =0.8011364
## class counts: 81 60
## probabilities: 0.574 0.426
## left son=4 (28 obs) right son=5 (113 obs)
## Primary splits:
## med_sickdays_hhave < 0.08333333 to the left, improve=5.583452, (0 missing)
## ed_expenses < 45.48365 to the left, improve=5.579527, (0 missing)
## cons_ed < 3.790304 to the left, improve=4.362527, (0 missing)
## cons_social < 0.1648248 to the right, improve=3.451186, (0 missing)
## asset_land_owned_total < 1.25 to the right, improve=2.760732, (0 missing)
## Surrogate splits:
## cons_alcohol < 4.186875 to the right, agree=0.816, adj=0.071, (0 split)
## cons_med_children < 7.206916 to the right, agree=0.809, adj=0.036, (0 split)
##
## Node number 3: 35 observations
## predicted class=1 expected loss=0.2 P(node) =0.1988636
## class counts: 7 28
## probabilities: 0.200 0.800
##
## Node number 4: 28 observations
## predicted class=0 expected loss=0.1428571 P(node) =0.1590909
## class counts: 24 4
## probabilities: 0.857 0.143
##
## Node number 5: 113 observations, complexity param=0.05113636
## predicted class=0 expected loss=0.4955752 P(node) =0.6420455
## class counts: 57 56
## probabilities: 0.504 0.496
## left son=10 (102 obs) right son=11 (11 obs)
## Primary splits:
## ed_expenses < 45.48365 to the left, improve=4.167589, (0 missing)
## ed_schoolattend < 0.7321429 to the left, improve=3.073525, (0 missing)
## cons_allfood < 150.3553 to the left, improve=3.063232, (0 missing)
## cons_ed < 3.790304 to the left, improve=3.063232, (0 missing)
## cons_nondurable < 155.5233 to the left, improve=2.758684, (0 missing)
## Surrogate splits:
## cons_ed < 3.790304 to the left, agree=0.991, adj=0.909, (0 split)
## cons_social < 10.10303 to the left, agree=0.929, adj=0.273, (0 split)
##
## Node number 10: 102 observations, complexity param=0.05113636
## predicted class=0 expected loss=0.4509804 P(node) =0.5795455
## class counts: 56 46
## probabilities: 0.549 0.451
## left son=20 (33 obs) right son=21 (69 obs)
## Primary splits:
## cons_social < 0.7607301 to the right, improve=3.100054, (0 missing)
## cons_med_children < 2.80633 to the right, improve=1.844910, (0 missing)
## asset_durable < 157.351 to the right, improve=1.593137, (0 missing)
## cons_nondurable < 55.43596 to the right, improve=1.551191, (0 missing)
## cons_allfood < 27.7962 to the right, improve=1.551191, (0 missing)
## Surrogate splits:
## cons_nondurable < 55.43596 to the right, agree=0.902, adj=0.697, (0 split)
## cons_allfood < 27.7962 to the right, agree=0.902, adj=0.697, (0 split)
## ent_total_cost < 0.03336535 to the right, agree=0.892, adj=0.667, (0 split)
## durable_investment < 42.50397 to the right, agree=0.892, adj=0.667, (0 split)
## nondurable_investment < 0.7240282 to the right, agree=0.892, adj=0.667, (0 split)
##
## Node number 11: 11 observations
## predicted class=1 expected loss=0.09090909 P(node) =0.0625
## class counts: 1 10
## probabilities: 0.091 0.909
##
## Node number 20: 33 observations
## predicted class=0 expected loss=0.2727273 P(node) =0.1875
## class counts: 24 9
## probabilities: 0.727 0.273
##
## Node number 21: 69 observations, complexity param=0.03409091
## predicted class=1 expected loss=0.4637681 P(node) =0.3920455
## class counts: 32 37
## probabilities: 0.464 0.536
## left son=42 (61 obs) right son=43 (8 obs)
## Primary splits:
## hh_children < 2.5 to the left, improve=2.077037, (0 missing)
## cons_ed < 0.3002882 to the left, improve=1.627315, (0 missing)
## fs_chwholed_often < 0.3434622 to the right, improve=1.620659, (0 missing)
## cons_med_children < 0.6880889 to the right, improve=1.489211, (0 missing)
## years_of_edu < 10.5 to the right, improve=1.196034, (0 missing)
## Surrogate splits:
## cons_ed < 0.3002882 to the left, agree=0.971, adj=0.750, (0 split)
## cons_other < 20.05925 to the left, agree=0.971, adj=0.750, (0 split)
## ed_schoolattend < 0.25 to the left, agree=0.971, adj=0.750, (0 split)
## ed_expenses < 3.603458 to the left, agree=0.957, adj=0.625, (0 split)
## nondurable_investment < 0.854153 to the left, agree=0.957, adj=0.625, (0 split)
##
## Node number 42: 61 observations, complexity param=0.03409091
## predicted class=0 expected loss=0.4918033 P(node) =0.3465909
## class counts: 31 30
## probabilities: 0.508 0.492
## left son=84 (40 obs) right son=85 (21 obs)
## Primary splits:
## age < 26.5 to the right, improve=1.0370410, (0 missing)
## household_size < 4.5 to the right, improve=1.0089660, (0 missing)
## med_sickdays_hhave < 1.6844 to the left, improve=0.9841780, (0 missing)
## years_of_edu < 10.5 to the right, improve=0.7503067, (0 missing)
## marital_status < 0.5 to the right, improve=0.5608942, (0 missing)
## Surrogate splits:
## household_size < 4.5 to the right, agree=0.738, adj=0.238, (0 split)
## children < 2.5 to the right, agree=0.721, adj=0.190, (0 split)
## fs_chwholed_often < 0.2787356 to the right, agree=0.721, adj=0.190, (0 split)
## fs_meat < 1.5 to the right, agree=0.689, adj=0.095, (0 split)
## med_sickdays_hhave < 2.018315 to the left, agree=0.689, adj=0.095, (0 split)
##
## Node number 43: 8 observations
## predicted class=1 expected loss=0.125 P(node) =0.04545455
## class counts: 1 7
## probabilities: 0.125 0.875
##
## Node number 84: 40 observations, complexity param=0.02272727
## predicted class=0 expected loss=0.425 P(node) =0.2272727
## class counts: 23 17
## probabilities: 0.575 0.425
## left son=168 (20 obs) right son=169 (20 obs)
## Primary splits:
## cons_med_children < 1.249358 to the right, improve=1.2500000, (0 missing)
## age < 35.5 to the left, improve=0.8632832, (0 missing)
## children < 3.5 to the left, improve=0.8632832, (0 missing)
## fs_chwholed_often < 0.3642956 to the left, improve=0.2317043, (0 missing)
## household_size < 6.5 to the left, improve=0.1928571, (0 missing)
## Surrogate splits:
## children < 3.5 to the left, agree=0.825, adj=0.65, (0 split)
## med_sickdays_hhave < 1.525668 to the right, agree=0.800, adj=0.60, (0 split)
## fs_chwholed_often < 0.3642956 to the left, agree=0.775, adj=0.55, (0 split)
## household_size < 5.5 to the left, agree=0.725, adj=0.45, (0 split)
## years_of_edu < 8.5 to the left, agree=0.625, adj=0.25, (0 split)
##
## Node number 85: 21 observations
## predicted class=1 expected loss=0.3809524 P(node) =0.1193182
## class counts: 8 13
## probabilities: 0.381 0.619
##
## Node number 168: 20 observations
## predicted class=0 expected loss=0.3 P(node) =0.1136364
## class counts: 14 6
## probabilities: 0.700 0.300
##
## Node number 169: 20 observations, complexity param=0.01136364
## predicted class=1 expected loss=0.45 P(node) =0.1136364
## class counts: 9 11
## probabilities: 0.450 0.550
## left son=338 (7 obs) right son=339 (13 obs)
## Primary splits:
## age < 42.5 to the right, improve=0.3175824, (0 missing)
## children < 5 to the left, improve=0.1500000, (0 missing)
## household_size < 6.5 to the left, improve=0.1500000, (0 missing)
## years_of_edu < 9.5 to the left, improve=0.1000000, (0 missing)
## cons_med_children < 1.136585 to the left, improve=0.1000000, (0 missing)
## Surrogate splits:
## children < 3 to the left, agree=0.80, adj=0.429, (0 split)
## cons_med_children < 0.1501441 to the left, agree=0.80, adj=0.429, (0 split)
## fs_chwholed_often < 0.1666667 to the left, agree=0.80, adj=0.429, (0 split)
## cons_nondurable < 49.48167 to the right, agree=0.75, adj=0.286, (0 split)
## asset_durable < 69.1864 to the right, agree=0.75, adj=0.286, (0 split)
##
## Node number 338: 7 observations
## predicted class=0 expected loss=0.4285714 P(node) =0.03977273
## class counts: 4 3
## probabilities: 0.571 0.429
##
## Node number 339: 13 observations
## predicted class=1 expected loss=0.3846154 P(node) =0.07386364
## class counts: 5 8
## probabilities: 0.385 0.615
##
## n= 176
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 176 88 0 (0.50000000 0.50000000)
## 2) years_of_edu>=6.5 141 60 0 (0.57446809 0.42553191)
## 4) med_sickdays_hhave< 0.08333333 28 4 0 (0.85714286 0.14285714) *
## 5) med_sickdays_hhave>=0.08333333 113 56 0 (0.50442478 0.49557522)
## 10) ed_expenses< 45.48365 102 46 0 (0.54901961 0.45098039)
## 20) cons_social>=0.7607301 33 9 0 (0.72727273 0.27272727) *
## 21) cons_social< 0.7607301 69 32 1 (0.46376812 0.53623188)
## 42) hh_children< 2.5 61 30 0 (0.50819672 0.49180328)
## 84) age>=26.5 40 17 0 (0.57500000 0.42500000)
## 168) cons_med_children>=1.249358 20 6 0 (0.70000000 0.30000000) *
## 169) cons_med_children< 1.249358 20 9 1 (0.45000000 0.55000000)
## 338) age>=42.5 7 3 0 (0.57142857 0.42857143) *
## 339) age< 42.5 13 5 1 (0.38461538 0.61538462) *
## 85) age< 26.5 21 8 1 (0.38095238 0.61904762) *
## 43) hh_children>=2.5 8 1 1 (0.12500000 0.87500000) *
## 11) ed_expenses>=45.48365 11 1 1 (0.09090909 0.90909091) *
## 3) years_of_edu< 6.5 35 7 1 (0.20000000 0.80000000) *
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 19 15
## 1 18 22
##
## Accuracy : 0.5541
## 95% CI : (0.4339, 0.6698)
## No Information Rate : 0.5
## P-Value [Acc > NIR] : 0.2080
##
## Kappa : 0.1081
##
## Mcnemar's Test P-Value : 0.7277
##
## Sensitivity : 0.5135
## Specificity : 0.5946
## Pos Pred Value : 0.5588
## Neg Pred Value : 0.5500
## Prevalence : 0.5000
## Detection Rate : 0.2568
## Detection Prevalence : 0.4595
## Balanced Accuracy : 0.5541
##
## 'Positive' Class : 0
##